For any $2 \times 2$ matrix, if $A(a d j A)=\left[\begin{array}{cc}100 & 0 \\ 0 & 100\end{array}\right]$, then $|A|$ is equal to:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100
$A(adj\, A)=|A|I_2$
so $\begin{bmatrix}|A|&0\\0&|A|\end{bmatrix}=\begin{bmatrix}100&0\\0&100\end{bmatrix}$
$⇒|A|=100$