Question

If A is a $3\times 3$ non-singular matrix such that $A{A}^{\prime }=A^{\prime }A$ and $B=A^{-1}{A}^{\prime }$ then BB' equals

• A. I + B
• B. I
• C. $B^{-1}$
• D. $\left(B^{-1}\right)$

Answer 1

The correct option is B I

$B=A^{-1}{A}^{\prime }\Rightarrow AB=A^{\prime }AB{B}^{\prime }=A^{\prime }{B}^{\prime }=(BA{)}^{\prime }=(A^{-1}{A}^{\prime }A)=(A^{-1}A{A}^{\prime })=A\Rightarrow B{B}^{\prime }=I$