Example 13 If 
2 3
1
2
3
A
and B
4 5
4
2
5
2 1


−




=
=




−





, then find AB, BA Show that
AB ≠ BA Solution Since A is a 2 × 3 matrix and B is 3 × 2 matrix Hence AB and BA are both
defined and are matrices of order 2 × 2 and 3 × 3, respectively