Prove that if a and b are two matrices such that a+b and a*b are both defined, then a and b are square matrices

To multiply two matrices, i.e. of dimensions (mxn) and (nxp), the number of columns of the first matrix (n) must equal the number of rows of the second matrix (n), and to add two matrices together, their rows and columns must be equal.  Then both must be square matrices.