If for any 2 2 square matrix A, A(adj A) = 8 & 0 0 & 8 , then wri… - Vidyadip

Question

If for any $2 \times 2$ square matrix A, A(adj A) $= \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix},$ then write the value of |A|.

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Answer

it is given that
$\Rightarrow \text{A (adj A}) = 8 \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
$ \Rightarrow \text{A(adj A) } 8\text{I}_{2} \text{ }\text{ }\text{ } \dots\dots \text{(1)}$
We know that for any square matrix A of order 2, we have
$\text{A(adj A)} = |\text{A}| \text{I}_{2} \text{ }\text{ }\text{ } \dots\dots\dots \text{(2)}$
From (1) and (2), we have
|A| = 8

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