For a $3 × 3$ matrix A, if $A (adj A)=\begin{bmatrix} 99 & 0 & 0\\0 & 99 & 0\\0 & 0 & 99 \end{bmatrix}$ then $det(A)$ is equal to :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 99
$A \,adj\, A=|A|I$
so $A (adj A)=\begin{bmatrix} 99 & 0 & 0\\0 & 99 & 0\\0 & 0 & 99 \end{bmatrix}=|A|\begin{bmatrix} 1& 0 & 0\\0 & 1& 0\\0 & 0 & 1\end{bmatrix}$
$⇒|A|=99$