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

The correct option is B $$\mathrm{A}\mathrm{B},\ \mathrm{B}\mathrm{A}$$ exist and are not equal
Since, 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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