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 Note that
2 3
1
2
3
AB
4 5
4
2
5
2 1


−

 

= 
 

−
 



 =  
2
8
6
3 10
3
0
4
8
8
10
12
10
5
10
3
−
+
−
+
−




=




− +
+
−
+
+




and
2 3
2 12
4
6
6
15
1
2
3
BA
4 5
4
20
8 10
12
25
4
2
5
2 1
2
4
4
2
6
5
−
− +
+




−






=
=
−
− +
+






−





−
− +
+




 
10
2
21
16
2
37
2
2
11
−



= −




−
−


Clearly AB ≠ BA
In the above example both AB and BA are of different order and so AB ≠ BA