1) Use the equality:
In a similar way you can prove the general case.
2) The equality is not true for all A and B.
For example, if then
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.
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)
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!