Question

If $A$ is a square matrix of order $3$ such that $A(adj.A)=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]$, then find $\mid$ adj. $A\mid$.

Answer 1

Answer: 4.00

$|A\cdot adjA|=8$
$|A||adjA|=8$
$\Rightarrow |A{|}^3=8$
$\Rightarrow |A|=2$
$\Rightarrow |adjA|=4$