Let the determinant of a $3 imes 3$ matrix $A$ be 6, then $B$ is a matrix defined by $B = 5A^{2}$. Then, determinant of $B$ is

Question

Let the determinant of a $3 	imes 3$ matrix $A$ be 6, then $B$ is a matrix defined by $B = 5A^{2}$. Then, determinant of $B$ is

Dr. Abubacker · Accepted Answer

(d)
$B = 5A^{2}$
$\Rightarrow \det(B) = \det\left( 5A^{2} \right) = 5^{3}\left\lbrack \det(A) \right\rbrack^{2}$
$= 125(6)^{2} = 4500\ \ \ \ \ \lbrack given\det{A = 6\rbrack}$

Q. Let the determinant of a $3 \times 3$ matrix $A$ be 6, then $B$ is a matrix defined by $B = 5A^{2}$. Then, determinant of $B$ is

Explanation

Reviewed by Dr. Abubacker

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