Allied & ICAR Exam Bank • ALLIED_0011 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

If $A$ and $B$ are square matrices of the same order, which of the following is NOT generally valid?

Options:

  • (A) $AB = BA$
  • (B) $(AB)^T = B^T A^T$
  • (C) $\det(AB) = \det(A)\det(B)$
  • (D) $(AB)^{-1} = B^{-1} A^{-1}$

Answer Key:

A

Step-by-Step Solution & Explanation

Matrix multiplication is generally not commutative, so $AB \ne BA$ in general.
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