If $A = \begin{bmatrix}1&2\\0&3\end{bmatrix}$, then $|A\, adj\,A|$ is

9

The correct answer is Option (3) → 9 **

Given:

$A=\begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}$

For any square matrix:

$|A\,\text{adj}\,A| = |A|^{n}$ for an $n\times n$ matrix.

Here $n=2$.

Compute $|A|$:

$|A| = 1\cdot 3 - 2\cdot 0 = 3$

Thus:

$|A\,\text{adj}\,A| = |A|^{2} = 3^{2} = 9$