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Transpose of a Matrix

Let A3× m and...

Question

Let $A_{3 \times m}$ and $B_{4 \times n}$ be the two matrices such that $A B$ and $B A$ exist. Then the value of $m + n$ is

A

6

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B

7

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C

8

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D

5

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Solution

The correct option is B $7$
$A_{3 \times m}, B_{4 \times n} \Rightarrow (A B)_{3 \times n}$ exists, if $m = 4$

$B_{4 \times n}, A_{3 \times m} \Rightarrow (B A)_{4 \times m}$ exists, if $n = 3$
$∴ m + n = 7$

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Transpose of a Matrix

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