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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
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

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

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