Question

Let $[A{]}_{2\times 2}$ and $[B{]}_{3\times 3}$ be the two matrices such that $det\left(A\right)=2$ and $det\left(B\right)=3.$ Then the value of $det(det(A)\cdot B)+det(det(B)\cdot A)$ is

• A. $42$
• B. $24$
• C. $48$
• D. $20$

Answer 1

The correct option is A $42$

Given:
$det\left(A\right)=2$ and $det\left(B\right)=3.$
$det(det(A)\cdot B)+det(det(B)\cdot A)$
$=det(2\cdot B)+det(3\cdot A)$
$=2^3\cdot det\left(B\right)+3^2\cdot det\left(A\right)$
$=8\cdot 3+9\cdot 2=24+18$
$=42$