Question 
Here, ( A ) is a ( 2 times 2 ) matrix and ( B ) is a ( 2 times 3 ) matrix. Clearly, the number of columns in ( A= ) number of rows in ( B ). ( therefore A B ) exists and it is a ( 2 times 3 ) matrix.
[
begin{aligned}
A B &=left[begin{array}{cc}
5 & 4
2 & 3
end{array}right]left[begin{array}{ccc}
3 & 5 & 1
6 & 8 & 4
end{array}right]
&=left[begin{array}{ccccc}
5 cdot 3+4 cdot 6 & 5 cdot 5+4 cdot 8 & 5 cdot 1+4-4 &
2 cdot 3+3 cdot 6 & 2 cdot 5+3 cdot 8 & 2 cdot 1+3 cdot 4
end{array}right.& &
&=left[begin{array}{ccc}
15+24 & 25+32 & 5+16
6+18 & 10+24 & 2+12
end{array}right]=left[begin{array}{ccc}
39 & 57 & 21
24 & 34 & 14
end{array}right]
end{aligned}
]
( operatorname{Again}, B ) is a ( 2 times 3 ) matrix and ( A ) is a ( 2 times 2 ) matrix.
( therefore ) number of columns in ( B eq ) number of rows in ( A )
So, ( B A ) does not exist. 
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EXAMPLE FA/5 53 5 17 and B = 12 31 16 8 4 find AB and BA whichever exists.
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