Question Bank • QB_EXP_EM_MAT_032 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 $\det(M) = 33$. The value of $\det(\operatorname{adj}(M))$ is ________ (answer in integer).

Answer Key:

1089

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 $\det(M) = 33$: $\det(\operatorname{adj}(M)) = (33)^{3-1} = (33)^2 = 1089$ Therefore, the answer is $1089$.
← Previous (QB_EXP_EM_MAT_029) Next (QB_EXP_EM_MAT_035) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test