Question

If $A$ and $B$ are square matrices of same order such that $\left|\right.A\left|\right.=\left|\right.B\left|\right.=1$ and $A\left(\right.adjA+adjB\left.\right)=B$ .
Then the value of $\left|\right.A+B\left|\right.$ is

• A. $1$
• B. $2$
• C. $4$
• D. None of these

Answer 1

Answer: (A)

$A\left(\right.adjA+adjB\left.\right)=B$
$\left|\right.A\left|\right.I+A\cdot adj\left(\right.B\left.\right)=B$
$\left(\right.I+Aadj\left(\right.B\left.\right)\left.\right)B=B^{2}$
$B+A\cdot \left|\right.B\left|\right.I=B^{2}$
$B+A=B^{2}$
$\left|\right.B+A\left|\right.=\left|\right.B\left|\right.^{2}=1$