{
  "title": "Addition and Subtraction of Matrices - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Two matrices can be added only if they have ______. ✅", "options": {"A": "same number of rows", "B": "same number of columns", "C": "same order", "D": "same elements"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If A = [1 2; 3 4] and B = [0 1; 1 0], then A + B = ? ➕", "options": {"A": "[1 3; 4 4]", "B": "[1 1; 4 4]", "C": "[1 3; 3 4]", "D": "[1 3; 4 5]"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "What is the additive identity for matrices? 0️⃣", "options": {"A": "Matrix with all 1's", "B": "Null matrix of same order", "C": "Identity matrix", "D": "Diagonal matrix"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If P = [5 -2; 1 3] and Q = [2 4; -1 0], then P - Q = ? ➖", "options": {"A": "[3 -6; 2 3]", "B": "[7 2; 0 3]", "C": "[3 2; 0 3]", "D": "[3 -6; 0 3]"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "For matrices, A + B = B + A shows ______ property. 🔄", "options": {"A": "Associative", "B": "Commutative", "C": "Distributive", "D": "Closure"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Find the sum: [2 0] + [1 4] = ? 🧮", "options": {"A": "[3 4]", "B": "[2 4]", "C": "[3 0]", "D": "[2 1]"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If C = [a b; c d] and D = [w x; y z], then C + D = ? 📊", "options": {"A": "[a+w b+x; c+y d+z]", "B": "[a+w b+y; c+x d+z]", "C": "[aw bx; cy dz]", "D": "[a+x b+w; c+z d+y]"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Given A = [7 2; 3 1] and B = [0 0; 0 0], then A + B = ? 0️⃣", "options": {"A": "[0 0; 0 0]", "B": "[7 2; 3 1]", "C": "[1 1; 1 1]", "D": "[7 0; 0 1]"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Which matrix added to [4 -1; 2 5] gives [0 0; 0 0]? ➖", "options": {"A": "[4 1; 2 5]", "B": "[-4 1; -2 -5]", "C": "[0 0; 0 0]", "D": "[1 1; 1 1]"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If X = [8 -3], Y = [-2 7], then X + Y = ? ➕", "options": {"A": "[6 4]", "B": "[10 -10]", "C": "[6 -10]", "D": "[10 4]"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Matrix addition is ______: (A+B)+C = A+(B+C). 🔗", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If M = [1 2 3; 4 5 6] (2×3), which can be added to M? ➕", "options": {"A": "[1 2; 3 4]", "B": "[1 2 3; 4 5 6; 7 8 9]", "C": "[1 2 3; 4 5 6]", "D": "[1 2; 4 5; 7 8]"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Subtract: [9 5; 2 1] - [3 2; 1 0] = ? ➖", "options": {"A": "[6 3; 1 1]", "B": "[12 7; 3 1]", "C": "[6 7; 1 1]", "D": "[6 3; 3 1]"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If A + B = O (null matrix), then B is called ______ of A. 🔄", "options": {"A": "Identity", "B": "Negative", "C": "Transpose", "D": "Symmetric"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Add: [0.5 1.2] + [1.5 0.8] = ? 🧮", "options": {"A": "[2.0 2.0]", "B": "[2.0 1.0]", "C": "[1.0 2.0]", "D": "[2.0 0.4]"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "For matrices of order 2×2, subtraction is defined if ______. ✅", "options": {"A": "both are square", "B": "both have same order", "C": "columns of first = rows of second", "D": "rows of first = columns of second"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If P - Q = [1 0; -2 3] and Q = [4 1; 0 -1], find P. 🔍", "options": {"A": "[5 1; -2 2]", "B": "[3 1; -2 4]", "C": "[5 1; -2 4]", "D": "[3 1; -2 2]"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "[a b] + [c d] = ? ✨", "options": {"A": "[a+c b+d]", "B": "[ac bd]", "C": "[a b c d]", "D": "[a+c, b+d]"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If A = [x 2; 3 y], B = [1 -2; 3 4], and A+B = [2 0; 6 6], find x,y. 🧩", "options": {"A": "x=1, y=2", "B": "x=1, y=4", "C": "x=2, y=1", "D": "x=3, y=2"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Which is true? A - B = ______. ❌", "options": {"A": "B - A", "B": "-(B - A)", "C": "A + B", "D": "B + A"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "If A = [2 5; -1 3], B = [0 4; 2 -2], then 2A - 3B = ? 🔢", "options": {"A": "[4 -2; -8 12]", "B": "[4 -2; -4 12]", "C": "[4 2; -8 12]", "D": "[4 -2; -8 0]"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Given A+B = [7 1; 4 9] and A-B = [1 3; -2 1], find A. ➕➖", "options": {"A": "[4 2; 1 5]", "B": "[3 1; 2 4]", "C": "[4 2; 1 4]", "D": "[3 2; 1 5]"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If matrix X + [2 0; -1 3] = [5 1; 2 8], find X. 🔍", "options": {"A": "[3 1; 3 5]", "B": "[7 1; 1 11]", "C": "[3 1; 1 5]", "D": "[7 1; 3 5]"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "For matrices A, B, C of same order, (A - B) + C = ? 🔗", "options": {"A": "A - (B + C)", "B": "A + C - B", "C": "C - B + A", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "If P = [1 2; 3 4], Q = [5 6; 7 8], find 3P - 2Q. 🧮", "options": {"A": "[-7 -6; -5 -4]", "B": "[-7 -6; -5 -8]", "C": "[13 18; 23 28]", "D": "[-7 -6; -10 -8]"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Given A = [a 2b; 3c d], B = [3a b; c 2d], and A+B = [8 9; 7 9], find a,b,c,d. 🧩", "options": {"A": "a=2,b=3,c=1,d=3", "B": "a=1,b=3,c=2,d=3", "C": "a=2,b=1,c=3,d=3", "D": "a=1,b=2,c=3,d=3"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Which is not possible? ❌", "options": {"A": "[1 2] + [3 4]", "B": "[[1];[2]] + [[3];[4]]", "C": "[1 2 3] + [4 5]", "D": "[1 2;3 4] + [0 0;0 0]"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "If M is 2×3, N is 2×3, then M - N is of order ______. 📐", "options": {"A": "2×3", "B": "3×2", "C": "2×2", "D": "3×3"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Find X if X + [1 -2; 0 4] = [3 1; -2 0]. ➕", "options": {"A": "[2 3; -2 -4]", "B": "[4 -1; -2 -4]", "C": "[2 3; 2 -4]", "D": "[2 3; -2 4]"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If A = [p+2 3; 4 q-1], B = [3 3; 4 4], and A=B, find p,q. 🔍", "options": {"A": "p=1, q=5", "B": "p=5, q=1", "C": "p=1, q=1", "D": "p=5, q=5"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Subtract the matrix [0.3 1.2; 4.5 2.1] from [1.0 2.0; 5.0 3.0]. ➖", "options": {"A": "[0.7 0.8; 0.5 0.9]", "B": "[1.3 3.2; 9.5 5.1]", "C": "[0.7 0.8; 1.5 1.9]", "D": "[0.7 -0.8; -0.5 0.9]"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If (A + B) = [5 7; 1 0] and A = [2 4; -3 2], find B. ➕", "options": {"A": "[3 3; 4 -2]", "B": "[7 11; -2 2]", "C": "[3 3; -4 -2]", "D": "[3 3; 4 2]"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "For A = [1 0; 0 1], B = [0 1; 1 0], find (A+B) - (A-B). 🔄", "options": {"A": "[0 2; 2 0]", "B": "[2 0; 0 2]", "C": "[1 1; 1 1]", "D": "[0 0; 0 0]"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Given C - D = [4 -1; 0 2] and C + D = [6 3; 2 0], find C. ➕➖", "options": {"A": "[5 1; 1 1]", "B": "[10 2; 2 2]", "C": "[5 1; 2 1]", "D": "[5 2; 1 1]"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "If M = [[1,2],[3,4],[5,6]] (3×2), what is M - M? ➖", "options": {"A": "M", "B": "Null matrix 3×2", "C": "Identity 3×2", "D": "Not defined"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Find k if [k 2; 3 4] + [1 -2; 3 0] = [3 0; 6 4]. 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "If X + Y = Z, then X = ______. ➕", "options": {"A": "Z + Y", "B": "Z - Y", "C": "Y - Z", "D": "Z × Y"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Given P = [a b; c d], Q = [e f; g h], find P + Q - P. ➕➖", "options": {"A": "Q", "B": "P", "C": "Null matrix", "D": "Identity"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If A = [x+y 2; 5 z-1] and B = [3 2; 5 3], A = B, find x,y,z. 🧩", "options": {"A": "x=1,y=2,z=4", "B": "x=2,y=1,z=4", "C": "x=3,y=0,z=4", "D": "x=0,y=3,z=4"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "Add: [[2],[4],[6]] + [[1],[3],[5]] = ? ➕", "options": {"A": "[3 7 11]", "B": "[3; 7; 11]", "C": "[2 4 6; 1 3 5]", "D": "[3 12 30]"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "If A = [1 2; 3 4], B = [2 0; 1 3], C = [0 1; 2 4], find (A+B) - C. ➕➖", "options": {"A": "[3 1; 2 3]", "B": "[1 3; 2 3]", "C": "[3 1; 4 7]", "D": "[3 3; 2 3]"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Given 2A - B = [4 6; 8 10] and A + B = [5 3; 7 5], find A and B. 🧮", "options": {"A": "A=[3 3; 5 5], B=[2 0; 2 0]", "B": "A=[3 3; 5 5], B=[2 1; 2 1]", "C": "A=[3 3; 4 4], B=[2 0; 3 1]", "D": "A=[2 3; 4 5], B=[3 0; 3 0]"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "If P = [a b; c d], Q = [b a; d c], find P + Q - [a+b 0; 0 c+d]. 🔄", "options": {"A": "[0 0; 0 0]", "B": "[a b; c d]", "C": "[b a; d c]", "D": "[a+b a+b; c+d c+d]"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "For matrices A, B, C of same order, solve for X: X + A = B - C. 🧩", "options": {"A": "X = B - C - A", "B": "X = B - C + A", "C": "X = A + B + C", "D": "X = B + C - A"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "If M = [1 -1; 2 0], N = [0 2; -1 1], find 3M - 2N + 4I (I is identity). ✨", "options": {"A": "[7 -7; 8 2]", "B": "[7 -7; 8 -2]", "C": "[3 -7; 8 2]", "D": "[7 1; 8 2]"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Given A + B = [2 4 6; 8 10 12], A - B = [0 2 4; 6 8 10], find A. ➕➖", "options": {"A": "[1 3 5; 7 9 11]", "B": "[2 6 10; 14 18 22]", "C": "[1 1 1; 1 1 1]", "D": "[0 2 4; 6 8 10]"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "If X and Y are 3×2 matrices, can we compute X - Y + Z where Z is 2×3? ❌", "options": {"A": "Yes", "B": "No", "C": "Only if Z transpose", "D": "Only if square"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "For A = [p q; r s], B = [p -q; -r s], find A + B. ➕", "options": {"A": "[2p 0; 0 2s]", "B": "[p q; r s]", "C": "[0 0; 0 0]", "D": "[2p 2q; 2r 2s]"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If [x y; z w] + [1 2; 3 4] = [4 3; 2 1], find x,y,z,w. 🔢", "options": {"A": "x=3,y=1,z=-1,w=-3", "B": "x=5,y=5,z=5,w=5", "C": "x=3,y=1,z=5,w=5", "D": "x=3,y=1,z=-1,w=5"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Given 3×3 matrices A,B,C with A+B=C and B+C=A, find C. 🔍", "options": {"A": "Null matrix", "B": "A", "C": "B", "D": "Identity"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "If P+Q = [5 0; -1 3], P-Q = [1 4; 3 -1], find 2P + 3Q. 🧮", "options": {"A": "[13 12; 7 3]", "B": "[8 4; 4 2]", "C": "[7 6; 1 0]", "D": "[13 12; 7 0]"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Solve for matrix X: X - [2 3; 1 4] = [1 -1; 0 2]. ➕", "options": {"A": "[3 2; 1 6]", "B": "[1 -4; -1 -2]", "C": "[3 4; 1 6]", "D": "[-1 -4; -1 -2]"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "If A = [1 2; 3 4], B = [5 6; 7 8], find (A+B) - (B+A). ➕➖", "options": {"A": "Null matrix", "B": "A", "C": "B", "D": "2A+2B"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Given A+B = [a 5; 2 b], A-B = [1 c; 4 3], find a,b,c if B is null matrix. 🔍", "options": {"A": "a=1,b=3,c=5", "B": "a=2,b=6,c=5", "C": "a=1,b=6,c=5", "D": "a=2,b=3,c=5"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "hard", "question": "If M = [2x 3y; 4z 5w], N = [x y; z w], and M+N = [9 12; 12 18], find x,y,z,w. 🧩", "options": {"A": "x=3,y=3,z=2,w=3", "B": "x=3,y=4,z=2,w=3", "C": "x=2,y=3,z=3,w=4", "D": "x=3,y=3,z=3,w=3"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "For any square matrix A, (A + Aᵀ) is ______ matrix. 📐", "options": {"A": "Symmetric", "B": "Skew-symmetric", "C": "Null", "D": "Identity"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If A = [0 1; -1 0], B = [0 -1; 1 0], find A+B and A-B. ➕➖", "options": {"A": "A+B=[0 0; 0 0], A-B=[0 2; -2 0]", "B": "A+B=[0 0; 0 0], A-B=[0 0; 0 0]", "C": "A+B=[0 2; -2 0], A-B=[0 0; 0 0]", "D": "A+B=[0 0; 0 0], A-B=[0 -2; 2 0]"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Given X+2Y = [7 2; 1 5] and X-Y = [1 -1; 4 2], find X. 🧮", "options": {"A": "[3 0; 3 3]", "B": "[5 1; 5 4]", "C": "[3 0; 5 3]", "D": "[5 1; 3 4]"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "If P,Q,R are 2×2 matrices and P+Q=R, Q+R=P, then R = ? 🔄", "options": {"A": "Null matrix", "B": "P", "C": "Q", "D": "P+Q"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "For A = [p q; r s], find B such that A+B is a scalar matrix trace 5. 🔢", "options": {"A": "[5-p -q; -r 5-s]", "B": "[5 0; 0 5]", "C": "[5-p 0; 0 5-s]", "D": "[5-p -q; -r s]"}, "correct_answer": "A"}
  ]
}