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  4. For a invertible matrix A if A ( textadj A )=[10 0 0 10], then | A |=

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Q. For a invertible matrix $A$ if $A (\text{adj} A )=\begin{bmatrix}10 & 0 \\ 0 & 10\end{bmatrix}$, then $| A |=$

MHT CETMHT CET 2017Determinants

Solution:

Given : $A (\text{adj} A )=\begin{bmatrix}10 & 0 \\ 0 & 10\end{bmatrix}=10\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}=10 I$
We know that, $A ^{-1}=\frac{1}{| A |} \text{Adj}( A )$
$ \Rightarrow A (\text{adj} A )=| A | I$
$\Rightarrow | A |=10$