If $A = [a_{ij}]$ is a square matrix of order 2 such that, $a_{ij} =\left\{\begin{matrix}2,&\text{when i ≠j}\\0,&\text{when i=j}\end{matrix}\right.$, then $det (A^2)$ is:

16

The correct answer is Option (4) → 16

Given that $A = [a_{ij}]$ is a square matrix of order 2 such that

$a_{ij} = \begin{cases} 2, & i \ne j \\ 0, & i = j \end{cases}$

Hence, $A = \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}$

$\det(A) = (0)(0) - (2)(2) = -4$

Now, $\det(A^2) = [\det(A)]^2 = (-4)^2 = 16$

Therefore, $\det(A^2) = 16$.