If $A$ is a square matrix of order 3 such that $A (adj\, A) =\begin{bmatrix}-2&0&0\\0&-2&0\\0&0&-2\end{bmatrix}$ then $|A|$ is equal to

-2

The correct answer is Option (4) → -2 **

For any square matrix $A$ of order $3$:

$A(\text{adj}\,A) = |A|\,I$

Given:

$A(\text{adj}\,A) = \begin{bmatrix}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$

This equals $|A|\,I$.

So,

$|A|\,I = -2I$

Thus,

$|A| = -2$

The value of $|A|$ is $-2$.