Allied & ICAR Exam Bank • ALLIED_1037 NAT • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Determinants

Question Statement:

If $A$ is a $3 \times 3$ matrix with $\det(A) = 4$, then the determinant of the matrix $2A$ is:

Answer Key:

32

Step-by-Step Solution & Explanation

For an $n \times n$ matrix $A$, $\det(k A) = k^n \det(A)$. Here $n = 3$, so $\det(2A) = 2^3 \det(A) = 8 \times 4 = 32$.
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