Question

Let A be a square matrix of order n and B be its adjoint, then for a scalar K, $|AB+K{I}_n|$ is ___

• A. $(|A|+K{)}^{n-2}$
• B. $(|A|+K{)}^n$
• C. $(|A|+K{)}^{n-1}$
• D. None of these

Answer 1

The correct option is B

$(|A|+K{)}^n$

We have AB = A(adj A) $=|A|I_n$
$\therefore AB+K{I}_n=|A|I_n+K{I}_n\Rightarrow AB+K{I}_n=(|A|+K)I_n\Rightarrow |AB+K{I}_n|=|(|A|+K)I_n|=(|A|+K{)}^n$