Question

If A is a 3 × 4 matrix and B is a matrix such that both A^TB and BA^T are defined, what is the order of the matrix B?

Answer 1

A is a matrix of order 3 × 4

So A^T will be a matrix of order 4 × 3

A^TB will be defined when B is a matrix of order 3 × n

BA^T will be defined when B is of order m × 4

From (1) and (2) we see that B should be a matrix of order 3 × 4