Question
If $\text{A}=\begin{bmatrix}2&4&-1\\-1&0&2\end{bmatrix},\text{B}=\begin{bmatrix}3&4\\-1&2\\2&1\end{bmatrix},$ find $(AB)^T$
✓
Answer
Here,
$\text{AB}=\begin{bmatrix}2&4&-1\\-1&0&2\end{bmatrix}\begin{bmatrix}3&4\\-1&2\\2&1\end{bmatrix}$
$\Rightarrow\text{AB}=\begin{bmatrix}6-4-2&8+8-1\\-3-0+4&-4+0+2\end{bmatrix}$
$\Rightarrow\text{AB}=\begin{bmatrix}0&15\\1&-2\end{bmatrix}$
$\Rightarrow(\text{AB})^\text{T}=\begin{bmatrix}0&1\\15&-2\end{bmatrix}$
$\text{AB}=\begin{bmatrix}2&4&-1\\-1&0&2\end{bmatrix}\begin{bmatrix}3&4\\-1&2\\2&1\end{bmatrix}$
$\Rightarrow\text{AB}=\begin{bmatrix}6-4-2&8+8-1\\-3-0+4&-4+0+2\end{bmatrix}$
$\Rightarrow\text{AB}=\begin{bmatrix}0&15\\1&-2\end{bmatrix}$
$\Rightarrow(\text{AB})^\text{T}=\begin{bmatrix}0&1\\15&-2\end{bmatrix}$
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