Matrices & Determinants Question - None

Question

Column I (A): If A is a square matrix of order 3 and $\det(A) = 3$, then $\det(6A^{-1})$ is divisible by

Column II: Match with the appropriate divisor from options (p), (q), (r), (s)

Accepted Answer

For statement A: If A is a square matrix of order 3 and $\det(A) = 3$, find $\det(6A^{-1})$.

$\det(6A^{-1}) = \det(6I \cdot A^{-1}) = 6^3 \cdot \det(A^{-1})$

Since $\det(A^{-1}) = \frac{1}{\det(A)} = \frac{1}{3}$

$\det(6A^{-1}) = 216 \cdot \frac{1}{3} = 72$

72 is divisible by 3.

A matches with (p) 3

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