Question

If A and B matrices commute then

• A. If $A^{-1}$ and $B$ also commute
• B. $B^{-1}$ and $A$ also commute
• C. $A^{-1}$ and $B^{-1}$ also commute
• D. all of the above

Answer 1

Answer: (C)

$A^{-1}$ and $B^{-1}$ also commute

we know that ${\left(CD\right)}^{-1}=D^{-1}{C}^{-1}$
$AB=BA\Rightarrow {\left(AB\right)}^{-1}={\left(BA\right)}^{-1}$
$\Rightarrow B^{-1}{A}^{-1}=A^{-1}{B}^{-1}$