Allied & ICAR Exam Bank • ALLIED_2601 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

Let $A$ be a $4 \times 4$ real matrix with $\det(A) = -3$. The determinant of the adjugate matrix $\text{adj}(A)$ is:

Options:

  • (A) -27
  • (B) 27
  • (C) -81
  • (D) 81

Answer Key:

A

Step-by-Step Solution & Explanation

For an $n \times n$ matrix $A$, $\det(\text{adj}(A)) = (\det(A))^{n-1}$. Here $n = 4$, so $\det(\text{adj}(A)) = (-3)^{4-1} = (-3)^3 = -27$.
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