{
  "title": "Multiplication of Matrices - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If A = [[2, 3]] and B = [[4], [5]], what is A × B? 📊", "options": {"A": "[[23]]", "B": "[[14]]", "C": "[[15]]", "D": "[[20]]"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is [[1, 2]] × [[3], [4]]? 🤔", "options": {"A": "[[11]]", "B": "[[10]]", "C": "[[12]]", "D": "[[9]]"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Multiply: [[3]] × [[5]] = ? ✖️", "options": {"A": "[[15]]", "B": "[[8]]", "C": "[[2]]", "D": "[[35]]"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "If A = [[1, 0]] and B = [[2], [3]], find A×B 🧮", "options": {"A": "[[2]]", "B": "[[3]]", "C": "[[5]]", "D": "[[0]]"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "What is [[2, 1]] × [[1], [2]]? 🔢", "options": {"A": "[[4]]", "B": "[[3]]", "C": "[[5]]", "D": "[[6]]"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "If P = [[4]] and Q = [[3]], find P×Q 💡", "options": {"A": "[[12]]", "B": "[[7]]", "C": "[[1]]", "D": "[[43]]"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "[[1, 2, 3]] × [[1], [0], [2]] = ? 🎯", "options": {"A": "[[7]]", "B": "[[6]]", "C": "[[5]]", "D": "[[8]]"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Multiply: [[0, 5]] × [[2], [1]] 📐", "options": {"A": "[[5]]", "B": "[[10]]", "C": "[[7]]", "D": "[[0]]"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "What is [[2]] × [[3, 4]]? ❌", "options": {"A": "Cannot multiply", "B": "[[6, 8]]", "C": "[[5]]", "D": "[[12]]"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "If A = [[1, 1]] and B = [[1], [1]], A×B = ? ➕", "options": {"A": "[[2]]", "B": "[[1]]", "C": "[[0]]", "D": "[[11]]"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "[[3, 2]] × [[1], [1]] = ? 🤓", "options": {"A": "[[5]]", "B": "[[6]]", "C": "[[4]]", "D": "[[3]]"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Multiply: [[2, 0]] × [[0], [5]] ⚡", "options": {"A": "[[0]]", "B": "[[10]]", "C": "[[7]]", "D": "[[5]]"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "What is [[1, 2, 3]] × [[2], [1], [1]]? 📈", "options": {"A": "[[7]]", "B": "[[6]]", "C": "[[8]]", "D": "[[9]]"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If A = [[4, 2]] and B = [[1], [2]], find A×B 🎲", "options": {"A": "[[8]]", "B": "[[6]]", "C": "[[10]]", "D": "[[12]]"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "[[5]] × [[2]] = ? ✨", "options": {"A": "[[10]]", "B": "[[7]]", "C": "[[3]]", "D": "[[52]]"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Multiply: [[1, 3]] × [[2], [2]] 🔄", "options": {"A": "[[8]]", "B": "[[6]]", "C": "[[7]]", "D": "[[9]]"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "What is [[0, 0]] × [[3], [4]]? 🎪", "options": {"A": "[[0]]", "B": "[[7]]", "C": "[[12]]", "D": "[[1]]"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "If A = [[2, 1]] and B = [[1], [3]], A×B = ? 📍", "options": {"A": "[[5]]", "B": "[[4]]", "C": "[[6]]", "D": "[[7]]"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "[[3, 1]] × [[2], [1]] = ? 🔢", "options": {"A": "[[7]]", "B": "[[5]]", "C": "[[4]]", "D": "[[8]]"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Multiply: [[1, 4]] × [[3], [0]] 🚀", "options": {"A": "[[3]]", "B": "[[4]]", "C": "[[7]]", "D": "[[12]]"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 2]], find A×B 🧩", "options": {"A": "[[4, 4], [10, 8]]", "B": "[[2, 4], [6, 8]]", "C": "[[3, 2], [7, 6]]", "D": "[[5, 4], [11, 8]]"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Find product: [[2, 1], [3, 4]] × [[1, 2], [0, 1]] 📦", "options": {"A": "[[2, 5], [3, 10]]", "B": "[[3, 4], [3, 7]]", "C": "[[2, 3], [4, 5]]", "D": "[[2, 4], [3, 8]]"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If A = [[0, 1], [2, 3]] and B = [[1, 0], [4, 5]], find B×A 🔄", "options": {"A": "[[0, 1], [8, 19]]", "B": "[[1, 3], [4, 15]]", "C": "[[2, 3], [14, 15]]", "D": "[[0, 2], [12, 17]]"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Multiply: [[1, 0, 2], [3, 1, 4]] × [[2], [1], [3]] 🎲", "options": {"A": "[[8], [19]]", "B": "[[7], [17]]", "C": "[[6], [15]]", "D": "[[9], [20]]"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If A = [[2, 3], [1, 4]] and B = [[1, 1], [2, 0]], find A² (A×A) 💥", "options": {"A": "[[7, 18], [6, 19]]", "B": "[[4, 9], [1, 16]]", "C": "[[5, 12], [4, 13]]", "D": "[[6, 15], [5, 16]]"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "What is [[1, 2, 3], [4, 5, 6]] × [[1], [2], [3]]? 🎯", "options": {"A": "[[14], [32]]", "B": "[[6], [15]]", "C": "[[12], [30]]", "D": "[[10], [25]]"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If A = [[3, -1], [2, 4]] and B = [[0, 2], [1, 3]], find A×B 🧮", "options": {"A": "[[-1, 3], [4, 16]]", "B": "[[3, 3], [2, 16]]", "C": "[[-1, 6], [4, 18]]", "D": "[[3, 5], [2, 14]]"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Find product: [[2, 0], [1, 3]] × [[1, 2], [4, 5]] ✨", "options": {"A": "[[2, 4], [13, 17]]", "B": "[[3, 4], [5, 11]]", "C": "[[2, 4], [5, 7]]", "D": "[[2, 0], [4, 15]]"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If P = [[1, 2], [0, 1]] and Q = [[2, 1], [3, 4]], find P×Q 🤔", "options": {"A": "[[8, 9], [3, 4]]", "B": "[[5, 6], [3, 4]]", "C": "[[7, 8], [3, 4]]", "D": "[[6, 7], [3, 4]]"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Multiply: [[a, b], [c, d]] × [[1, 0], [0, 1]] = ? 📊", "options": {"A": "[[a, b], [c, d]]", "B": "[[1, 0], [0, 1]]", "C": "[[b, a], [d, c]]", "D": "[[0, 0], [0, 0]]"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "If A = [[2, 1], [1, 3]] and B = [[3, 2], [1, 4]], find A×B 🔢", "options": {"A": "[[7, 8], [6, 14]]", "B": "[[5, 6], [4, 12]]", "C": "[[8, 9], [7, 15]]", "D": "[[6, 7], [5, 13]]"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "What is [[1, 0, 1], [2, 1, 3]] × [[2], [1], [1]]? 📈", "options": {"A": "[[3], [8]]", "B": "[[2], [6]]", "C": "[[4], [9]]", "D": "[[3], [7]]"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If A = [[4, 2], [1, 3]] and I = [[1, 0], [0, 1]], find A×I ⚡", "options": {"A": "[[4, 2], [1, 3]]", "B": "[[1, 0], [0, 1]]", "C": "[[5, 2], [1, 4]]", "D": "[[4, 3], [2, 3]]"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Find: [[x, y]] × [[2], [3]] = [[8]], find relation 🎪", "options": {"A": "2x + 3y = 8", "B": "x + y = 8", "C": "2x + y = 8", "D": "x + 3y = 8"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "If A = [[1, 2], [3, 4]] and B = [[0, 0], [0, 0]], A×B = ? 🚀", "options": {"A": "[[0, 0], [0, 0]]", "B": "[[1, 2], [3, 4]]", "C": "[[0, 2], [0, 4]]", "D": "[[1, 0], [3, 0]]"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Multiply: [[2, -1], [3, 4]] × [[1, 2], [-1, 3]] 💡", "options": {"A": "[[3, 1], [-1, 18]]", "B": "[[1, 1], [2, 12]]", "C": "[[3, 7], [7, 18]]", "D": "[[2, -2], [-3, 12]]"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If A = [[1, 0], [0, 1]] and B = [[5, 6], [7, 8]], A×B = ? 📍", "options": {"A": "[[5, 6], [7, 8]]", "B": "[[1, 0], [0, 1]]", "C": "[[6, 6], [7, 9]]", "D": "[[5, 7], [6, 8]]"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Find product: [[2, 3], [1, 2]] × [[2, 3], [1, 2]] 🔄", "options": {"A": "[[7, 12], [4, 7]]", "B": "[[4, 9], [1, 4]]", "C": "[[6, 10], [3, 5]]", "D": "[[5, 11], [3, 6]]"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If A = [[0, 2], [3, 1]] and B = [[1, 4], [2, 3]], find B×A 🎲", "options": {"A": "[[12, 6], [9, 7]]", "B": "[[2, 6], [9, 5]]", "C": "[[3, 8], [6, 9]]", "D": "[[8, 10], [11, 13]]"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Multiply: [[1, 2, 3]] × [[1, 0], [2, 1], [3, 2]]? ❌", "options": {"A": "Cannot multiply", "B": "[[14, 8]]", "C": "[[6, 3]]", "D": "[[10, 5]]"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "If A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] and B = [[9, 8, 7], [6, 5, 4], [3, 2, 1]], find A×B 🧠", "options": {"A": "[[30, 24, 18], [84, 69, 54], [138, 114, 90]]", "B": "[[25, 20, 15], [70, 60, 50], [115, 100, 85]]", "C": "[[35, 28, 21], [94, 77, 60], [153, 126, 99]]", "D": "[[40, 32, 24], [104, 85, 66], [168, 138, 108]]"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Find A³ if A = [[2, 0], [1, 3]] (A×A×A) 💥", "options": {"A": "[[8, 0], [26, 27]]", "B": "[[6, 0], [13, 27]]", "C": "[[8, 0], [13, 27]]", "D": "[[4, 0], [7, 9]]"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "If A = [[cosθ, -sinθ], [sinθ, cosθ]] and B = [[cosθ, sinθ], [-sinθ, cosθ]], find A×B 🌀", "options": {"A": "[[1, 0], [0, 1]]", "B": "[[cos²θ, sinθcosθ], [sinθcosθ, cos²θ]]", "C": "[[0, 1], [1, 0]]", "D": "[[cos2θ, sin2θ], [sin2θ, cos2θ]]"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Solve for x,y: [[1, 2], [3, 4]] × [[x], [y]] = [[5], [11]] 📐", "options": {"A": "x=1, y=2", "B": "x=2, y=1", "C": "x=3, y=1", "D": "x=1, y=3"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "If A = [[a, b], [c, d]] and A² = [[1, 0], [0, 1]], which relation holds? 🤯", "options": {"A": "a²+bc=1, d²+bc=1, ab+bd=0, ac+cd=0", "B": "a²+b²=1, c²+d²=1", "C": "a+d=1, bc=0", "D": "ad-bc=1"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Find [[1, 2, 1], [0, 1, 2], [2, 0, 1]] × [[2], [-1], [3]] 🔢", "options": {"A": "[[3], [5], [7]]", "B": "[[4], [3], [8]]", "C": "[[5], [4], [6]]", "D": "[[2], [6], [9]]"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "If A = [[2, 1], [1, 0]] and B = [[1, 2], [3, 4]], find (A+B)×(A-B) ⚡", "options": {"A": "[[1, -3], [-6, -5]]", "B": "[[3, 3], [4, 4]]", "C": "[[-1, -1], [-2, -2]]", "D": "[[5, 7], [7, 9]]"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "For A = [[x, 2], [3, y]] and A² = [[7, 6], [9, 10]], find x+y 🎯", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If AB = [[6, 10], [15, 25]] and A = [[2, 0], [3, 5]], find B 🧩", "options": {"A": "[[3, 2], [0, 5]]", "B": "[[2, 3], [4, 5]]", "C": "[[1, 2], [3, 4]]", "D": "[[3, 5], [2, 4]]"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Find [[1, -1], [2, 3]] × [[3, 1], [-2, 4]] × [[1, 0], [0, 1]] ✨", "options": {"A": "[[5, -3], [0, 14]]", "B": "[[3, -1], [2, 3]]", "C": "[[1, -1], [2, 3]]", "D": "[[3, 1], [-2, 4]]"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "If A×B = [[11, 5], [26, 12]] and A = [[3, 1], [7, 2]], find B 📊", "options": {"A": "[[4, 1], [-1, 2]]", "B": "[[2, 1], [3, 2]]", "C": "[[3, 2], [5, 1]]", "D": "[[4, 3], [2, 1]]"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "For matrices, (A×B)×C = A×(B×C) illustrates which property? 📚", "options": {"A": "Associative", "B": "Commutative", "C": "Distributive", "D": "Identity"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], find trace(A×B) 🔎", "options": {"A": "70", "B": "30", "C": "50", "D": "90"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Find [[2, 1, 0], [1, 0, 2], [0, 2, 1]] × [[1, 0, 1], [2, 1, 0], [0, 1, 2]] 🎲", "options": {"A": "[[4, 1, 2], [1, 2, 5], [5, 3, 2]]", "B": "[[3, 2, 1], [2, 3, 4], [4, 2, 3]]", "C": "[[5, 2, 3], [2, 4, 6], [6, 4, 3]]", "D": "[[2, 1, 0], [1, 0, 2], [0, 2, 1]]"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "If A² - 4A + 3I = 0 where A = [[2, 1], [1, 2]], verify 🧮", "options": {"A": "Satisfies", "B": "Doesn't satisfy", "C": "Partially satisfies", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Find [[a, 0, 0], [0, b, 0], [0, 0, c]]³ 💎", "options": {"A": "[[a³, 0, 0], [0, b³, 0], [0, 0, c³]]", "B": "[[3a, 0, 0], [0, 3b, 0], [0, 0, 3c]]", "C": "[[a, 0, 0], [0, b, 0], [0, 0, c]]", "D": "[[a², 0, 0], [0, b², 0], [0, 0, c²]]"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If A = [[1, 3], [2, 6]] and B = [[2, 4], [-1, -2]], find A×B 🚀", "options": {"A": "[[-1, -2], [-2, -4]]", "B": "[[5, 10], [10, 20]]", "C": "[[-1, 2], [2, -4]]", "D": "[[0, 0], [0, 0]]"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "For A = [[k, 2], [3, 4]], if A² = A, find k 🎪", "options": {"A": "-1", "B": "0", "C": "1", "D": "2"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "If A×B = 0 but A≠0 and B≠0, such matrices are called? 🤔", "options": {"A": "Zero divisors", "B": "Inverses", "C": "Identities", "D": "Transposes"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Find [[1, ω, ω²], [ω, ω², 1], [ω², 1, ω]]² where ω³=1 🔄", "options": {"A": "[[0, 0, 0], [0, 0, 0], [0, 0, 0]]", "B": "[[1, 1, 1], [1, 1, 1], [1, 1, 1]]", "C": "[[3, 0, 0], [0, 3, 0], [0, 0, 3]]", "D": "Identity matrix"}, "correct_answer": "A"}
  ]
}