| Example 1 |
Find AB and BA, if
and 
.
Solution:
| Example 2 |
 |
Find AB and BA, if
and 
.
Solution:
,
| Example 3 |
|
Find AB and BA, if
and 
.
Solution:
,
.
Note that the product of two non-zero matrices may be equal to a zero-matrix.
| Example 4 |
|
Find 
, if
.
Solution:
,
,
,
...
.
| Example 5 |
|
Let 
and 
be matrices of the second order.
Verify that 
.
Solution:
Hence, the desired result.
