Allied & ICAR Exam Bank • ALLIED_0021 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

If $A$ is an invertible $n \times n$ matrix, then $\det(A^{-1})$ equals:

Options:

  • (A) $1 / \det(A)$
  • (B) $-\det(A)$
  • (C) $(\det A)^n$
  • (D) $1$

Answer Key:

A

Step-by-Step Solution & Explanation

Since $A A^{-1} = I$, $\det(A) \det(A^{-1}) = \det(I) = 1 \implies \det(A^{-1}) = 1/\det(A)$.
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