1. Tardigrade
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  3. Mathematics
  4. The product [a b -b a][a -b b a] is equal to

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Q. The product $\begin{bmatrix}a & b \\ -b & a\end{bmatrix}\begin{bmatrix}a & -b \\ b & a\end{bmatrix}$ is equal to

Matrices

Solution:

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