Question

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

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

Answer 1

Answer: (A)

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