Two things must be true for two matrices to be equal.
The two matrices must be the same size.
Each corresponding entry must be equal.
If you are given a matrix and asked to compute its transpose, you can think of "the rows becoming columns" (or, vice versa, "the columns becoming rows"). If we start with an m x n matrix, its transpose will be n x m.
We can add or subtract two matrices when they are the same size. If they are not the same size, the addition or subtraction is not defined.
Check out the WebAssign Frequently Asked Questions page for the answer to this question.