Compute the indicated products: a & b -b & a a & -b & a - Vidyadip

Question

Compute the indicated products:$\begin{bmatrix}\text{a} & \text{b} \\-\text{b} & \text{a} \end{bmatrix}\begin{bmatrix}\text{a} & -\text{b} \\\text{b} & \text{a} \end{bmatrix}$

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Answer

$\begin{bmatrix}\text{a} & \text{b} \\-\text{b} & \text{a} \end{bmatrix}\begin{bmatrix}\text{a} & -\text{b} \\\text{b} & \text{a} \end{bmatrix}$$=\begin{bmatrix}\text{a(a)}+\text{b(b)}&\text{a(-b)}+\text{b(a)}\\ -\text{b(a)}+\text{a(b)}&\text{(-b)(-b)}+\text{a(a)}\end{bmatrix}$
$=\begin{bmatrix}\text{a}^2+\text{b}^2&0\\0&\text{b}^2+\text{a} ^2\end{bmatrix}$

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