Question Bank • QB_EXP_EM_MAT_023 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra: Matrices & Determinants

Subtopic: Inverse of matrix

Question Statement:

Let $M$ be a $3 \times 3$ non-singular matrix with $\det(M) = 24$. The value of $\det(\operatorname{adj}(M))$ is ________ (answer in integer).

Answer Key:

576

Step-by-Step Solution & Explanation

For an $n \times n$ non-singular matrix $M$, the determinant of its classical adjugate matrix $\operatorname{adj}(M)$ is given by: $\det(\operatorname{adj}(M)) = (\det(M))^{n-1}$ For order $n = 3$ and $\det(M) = 24$: $\det(\operatorname{adj}(M)) = (24)^{3-1} = (24)^2 = 576$ Therefore, the answer is $576$.
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