Question
Compute the following:
$\begin{bmatrix}\cos^2\text{x} & \sin^2\text{x} \\ \sin^2 \text{x} & \cos^2 \text{x} \end{bmatrix}+\begin{bmatrix}\sin^2\text{x}&\cos^2\text{x}\\ \cos^2\text{x}&\sin^2\text{x}\end{bmatrix} $

Answer

$\begin{bmatrix}\cos^2\text{x} & \sin^2\text{x} \\ \sin^2 \text{x} & \cos^2 \text{x} \end{bmatrix}+\begin{bmatrix}\sin^2\text{x}&\cos^2\text{x}\\ \cos^2\text{x}&\sin^2\text{x}\end{bmatrix} $
$=\begin{bmatrix}\text{cos}^2\text{x}+\sin^2\text{x}&\sin^2\text{x}+\cos^2\text{x}\\ \sin^2\text{x}+\cos^2\text{x}&\cos^2\text{x}+\sin^2\text{x}\end{bmatrix}=\begin{bmatrix}1&1\\1&1\end{bmatrix} $

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