Multiplying Matrices

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

Given A = the 2 by 2 matrix with elements 5, 7, negative 3, and 0, and B = the 2 by 2 matrix with elements 1, 2, 9, and negative 1, find the products AB and BA. What does this suggest about whether or not matrix multiplication is commutative?
Given A = the 2 by 3 matrix with elements 2, negative 1, 3, 0, 1, and 5, and B = the 3 by 3 matrix with elements 1, 0, 2, 0, 3, 4, negative 1, 5, and negative 3, find AB and BA.
Given A = the 2 by 2 matrix with elements 1, 0, 0, and negative 1, find A squared, A cubed, A to the fourth power, and A to the nth power
Given A = the 3 by 3 matrix with elements 1, 0, 0, 0, 2, 0, 0, 0, and 1, find A squared, A cubed, A to the fourth power, and A to the nth power
Given A = the 3 by 3 matrix with elements 1, 1, 1, 0, 0, 1, 0, 0, and 1, find A squared, A cubed, A to the fourth power, and A to the nth power