Matrices
ICSE · Class 12 · Mathematics
Most important questions from Matrices for ICSE Class 12 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Matrix addition A + B is defined only when:
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A and B have the same order
Matrix addition requires A and B to have the exact same order (same number of rows and same number of columns).
If A is a 2×3 matrix and B is a 3×4 matrix, the order of AB is:
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2×4
If A is m×p and B is p×n, then AB is m×n. Here A is 2×3 and B is 3×4, so AB is 2×4.
Matrix multiplication is commutative, i.e., AB = BA always.
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False
Matrix multiplication is NOT commutative. In general AB ≠ BA. Even when both products are defined and of the same order, they need not be equal.
The transpose of a matrix A = [a_ij]_{m×n} is:
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[a_ji]_{n×m}
Transpose swaps row and column indices: (A^T)_ij = a_ji. The order also swaps from m×n to n×m.
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