Since this is an assignment,youare expected to do it! Here are some hints.

I presume you have done this- it's almost trivial.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)

I presume you mean "A is invertible".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)

Go ahead an multiply out left and right sides. You should get the same result. The only difference between this and elementary algebra is that you have to be careful not to commute A and B.

This is also close to being trivial.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

Look at and . Of course since A and B commute, those must be equal.