I believe the majority of the class understands how to add and subtract matrices, but do not think some of them know how to multiply, square, and cube matrices.

To multiply two matrices, dimensions must match. The number of columns of the first matrix must match the number of rows in the second matrix. So a matrix dimension of 2*3 can not be multiplied by a matrix dimension of 2*4, but a matrix dimension of a 4*6 can be multiplied by another dimension of 6*3 because the first matrix has six rows. So the number of rows and columns match. For the result dimension it would be 4*3 because the number of rows in the first matrix and the number of columns in the second matrix are combined to form the result matrix dimension:

[[2, 3], [4, 1]] * [[1, 3], [3, 4]]=[[11, 18], [7, 16]]`

[[2, 3], [4, 1], [5, 6]] * [[1, 3], [3, 4]`=NOT POSSIBLE, because the number of columns in the first matrix does not match the number of rows in the second matrix.

When multiplying two matrices, all the columns of the second matrix must multiply the first row of the first matrix. The first number of the first row multiplies the first number of the first column in the second matrix. The second number of the first row of the first matrix multiplies the second number of the first column of the second matrix and the third and so on. Then the second row multiplies the first column and the second column; number by number. When a row multiplies a column, all numbers needs to added to form one number of the end matrix:

[[2, 3], [4, 1]] * [[1, 3], [3, 4]]= [[2*1+3*3], [2*3+3*4], [4*1+ 1*3], [4*3+1*4]=[[11, 18], [7, 16]]`

When squaring or cubing two matrices, the process is the same as the multiplication process. For example, [[2, 3],[2,3]`^2, is the same as [[2, 3],[2,3]`* [[2, 3],[2,3]`. When cubing matrices, first multiply the first two matrices, then multiply the product of the first two matrices to the third matrix.