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Scalar Matrix

If A=[ 1 2; 0...

Question

If $A = [\begin{matrix} 1 & 2 0 & 1 \end{matrix}]$ and $B = [\begin{matrix} 4 & 5 0 & 3 \end{matrix}],$ then the value of sum of principal diagonal elements of $A B$ is

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Solution

Given :
$A = [\begin{matrix} 1 & 2 0 & 1 \end{matrix}]$
and $B = [\begin{matrix} 4 & 5 0 & 3 \end{matrix}]$
Now,
$A B = [\begin{matrix} 1 & 2 0 & 1 \end{matrix}] [\begin{matrix} 4 & 5 0 & 3 \end{matrix}]$
$\Rightarrow A B = [\begin{matrix} 4 + 0 & 5 + 6 0 + 0 & 0 + 3 \end{matrix}] = [\begin{matrix} 4 & 11 0 & 3 \end{matrix}]$
$∴$ Sum of principal diagonal elements of $A B = 7$

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