1. Tardigrade
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  4. If A is a square matrix of order 3 such that A(a d j . A)=[2 0 0 0 2 0 0 0 2], then find mid adj. A mid.

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Q. If $A$ is a square matrix of order $3$ such that $A(a d j . A)=\begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{bmatrix}$, then find $\mid$ adj. $A \mid$.

Matrices

Solution:

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