Hi I have an assignment question as follows

A, B and C are ntimes n matrices such that AB=I and CA=I

show B= C (i have done this part)

b) i. A and B are n times n matrices that commute. Show A squared and B squared commute

ii. Give a generalisation of this result (without proof)

c. A and B are n times n matrices and n is invetible. Shoe

(A+B) A^-1(A-B)=(A-B)A^-1(A+B)

d. A and B are n times n invertible matrices that commute. Show that A^-1 and B^-1 also commute

it's fairly urgent-any help would be much appreciated

thanks