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Let matrix $\mathrm{B}$ be the adjoint of a square matrix $\mathrm{A}, \ell$ be the identitymatrix of same order as A. If $k(\neq 0)$ is the determinant of the matrix $\mathrm{A}$, then what is $\mathrm{AB}$ equal to?
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The correct answer is:
$\mathrm{k} \ell$
$\mathrm{B}=\mathrm{adj} \mathrm{A}, \mathrm{I}=$ Identity matrix, $|\mathrm{A}|=k$
$\mathrm{AB}=\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}| \mathrm{I}=k \mathrm{I}$
$\mathrm{AB}=\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}| \mathrm{I}=k \mathrm{I}$
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