If A is a square matrix of order 3 and |A| = 4, then |2A| equals
Notice that we verify 32 by full calculation: use standard identity, substitute, simplify step by step to reach 32.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
#scalar multiplication
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For matrices of the same dimension M, N, and scalar c, which one of these properties DOES NOT ALWAYS hold?
Think of it like this: complete solution: write formula, plug data, do arithmetic. Final value matches MN = NM. Simple and accurate.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A is a 2 × 2 matrix and |A| = 5, what is |5A| ? (| | denotes determinant)
Let's break it down: formula |kA|=kⁿ|A|, n=order. Here n=2, k=5, |A|=5. So |5A|=5²×5=25×5=125. Full calculation.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
