Zero matrix as the product of two non zero matrices
We know that, for real numbers a, b if ab = 0, then either a = 0 or b = 0 This need
not be true for matrices, we will observe this through an example Example 15 Find AB, if 
0
1
A
0
−2


= 



 and 
3
5
B
0
0


= 


 Solution We have 
0
1
3
5
0
0
AB
0
2
0
0
0
0
−

 



=
=

 




 


