Question

If A and B matrices commute then

(A) A^-1 and B also commute

(B) B^-1 and A also commute

(C) A^-1 and B^-1 also commute

(D) All the above  

Answer 1

Answer is (C) A^-1 and B^-1 also commute

A and B matrices commute so AB = BA.

A^-1 × B^-1 = (BA)^-1 = (AB)^-1 = B^-1 × A^-1

So, A^-1 and B^-1 also commute.