If A is a square matrix of order 2 such that A (adj A)

As we know that, $A(\operatorname{adj} A)=|A| I$.

But it is given that $A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$

$\Rightarrow A(\operatorname{adj} A)=10\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

$\Rightarrow A(\operatorname{adj} A)=10 I$

$\Rightarrow|A| I=10 I$

$\Rightarrow|A|=10$

Hence, $|A|=\underline{10}$.