Question

If $A$ is non-singular matrix of order $3$ and $\left|adjA\right|={\left|A\right|}^k$, then write the value of $k$.

Answer 1

We know $AadjA=detA,I_{n\times n}$

$\Rightarrow det\left(A\right).det\left(adjA\right)={\left(detA\right)}^n$

$\therefore \left|adjA\right|={\left|A\right|}^{n-1}$

$\therefore k=n-1$

$=3-1=2$