Question

Here ( A ) is a ( 3 times 2 ) matrix and ( B ) is a ( 2 times 2 ) matrix. Clearly, the number of columns in ( A ) equals the number of rows in ( B ) ( A B ) exists and it is a ( 3 times 2 ) matrix.
[
begin{aligned}
text { Now, } A B &=left[begin{array}{rr}
2 & -1
3 & 4
1 & 5
end{array}right]left[begin{array}{rr}
-1 & 3
2 & 1
end{array}right]
&=left[begin{array}{rr}
2 cdot(-1)+(-1) cdot 2 & 2 cdot 3+(-1) cdot 1
3 cdot(-1)+4 cdot 2 & 3 cdot 3+4 cdot 1
1 cdot(-1)+5 cdot 2 & 1 cdot 3+5 cdot 1
end{array}right]
&=left[begin{array}{rr}
-4 & 5
5 & 13
9 & 8
end{array}right]
end{aligned}
]
Further, ( B ) is a ( 2 times 2 ) matrix and ( A ) is a ( 3 times 2 ) matrix. So, the number of columns in ( B ) is not equal to the number of rows in ( A ). So, ( B A ) does not exist.

# 137 EXAMPLE 2 aurez v 12-17 If A = 3 4 and B = 1 5 m -[21]. Find AB. Dos BA estar find AB. Does BA exist?

Solution