I'm in a linear algebra class and I'm quite new to proofs... In my textbook there are quite a bit of questions that says to prove a bunch of properties and whatnot.

For example...

How would I go about proving

(A^T)^p = (A^p)^T

where p is a non-negative integer and A is a square matrix. (T = transposed)

Or

If A and B is a n x n matrix, prove that AB = BA

How do I prove these? Do I provide an example or something or do I have to do something with summation notation?

A hint/guide would be very helpful. Thanks in advance!