Question

# If $$A=\left[\begin{array}{lll}1 & -2 & 3\\-4 & 2 & 5\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3\\4 & 5\\2 & 1\end{array}\right],$$ then

A
AB, BA exist and equal
B
AB, BA exist and are not equal
C
AB exists and BA does not exist
D
AB does not exist and BA exists

Solution

## The correct option is B $$\mathrm{A}\mathrm{B},\ \mathrm{B}\mathrm{A}$$ exist and are not equalSince, we have $$A = 2 \times 3 , \: B = 3 \times 2$$So, both $$AB$$ and $$BA$$ exist.But both are not equal to each other because bith are if different order $$\because AB \rightarrow 2 \times 2$$ and $$BA \rightarrow 3 \times 3.$$Mathematics

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