Verify the transpose multiplication on matrix — task. Mathematics State Board, Class 10.

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Check ${(AB)}^T = B^T A^T$ if $A =\begin{bmatrix}
6 & 9 & 4\\
10 & 2 & 3
\end{bmatrix}, B = \begin{bmatrix}
5 & 4\\
13 & 6\\
2 & 6
\end{bmatrix}$

$AB$ matrix	$=$ $[\begin{array}{l} i & i \\ i & i \end{array}]$
${(AB)}^T$ matrix	$=$ $[\begin{array}{l} i & i \\ i & i \end{array}]$
$B^T$ matrix	$=$ $[\begin{array}{l} i & i & i \\ i & i & i \end{array}]$
$A^T$ matrix	$=$ $[\begin{array}{l} i & i \\ i & i \\ i & i \end{array}]$
$B^T A^T$ matrix	$=$ $[\begin{array}{l} i & i \\ i & i \end{array}]$

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\(AB\) matrix	\(=\) $[\begin{array}{l} i & i \\ i & i \end{array}]$
\({(AB)}^T\) matrix	\(=\) $[\begin{array}{l} i & i \\ i & i \end{array}]$
\(B^T\) matrix	\(=\) $[\begin{array}{l} i & i & i \\ i & i & i \end{array}]$
\(A^T\) matrix	\(=\) $[\begin{array}{l} i & i \\ i & i \\ i & i \end{array}]$
\(B^T A^T\) matrix	\(=\) $[\begin{array}{l} i & i \\ i & i \end{array}]$

9. Verify the transpose multiplication on matrix