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Multiplication of Matrices

Let two matri...

Question

Let two matrices $A$ and $B$ of order $2 \times (m + 2 n)$ and $8 \times n$ respectively. If the matrix multiplication $A B$ and $B A$ exist. Then the value of $m + n$ equals to

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Solution

For multiplication $A B$ existence : number of columns in $A =$ number of rows in $B$
$\Rightarrow m + 2 n = 8 \dots (i)$
and for multiplication $B A$ existence : number of columns in $B =$ number of rows in $A$
$\Rightarrow n = 2$
So, $m = 4, n = 2$ (from $(i)$ )
$∴ m + n = 6$

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Multiplication of Matrices

Standard XII Mathematics

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