ok thanks how bout this one
1)A and B are both m × n matrices. Are AB and BA defined and, if so, how many rows and
columns do they have?
2)The matrices A and B are 2 × 2 matrices, and O is the zero 2 × 2 matrix. Is the following
argument correct?
‘If AB = O, and A = O, then B = O’.
No they're not.
If matrix A was m x n and matrix B was n x m, they both would be.
AB would be m x m and BA would be n x n.
In general, if you have two matrices, I'll call them X and Y, they can only be multiplied together (in the form XY, not YX) if the number of columns in X and the number of rows in Y are equal. XY will have the same number of rows as X and the same number of columns as Y.