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Rotation of the plane $R^2$ counterclockwise around the origin by 90 degrees is a linear transformation from $R^2$ to $R^2$. What is the corresponding matrix?

From the previous question, write down the matrix A corresponding to rotation of the plane $R^2$ counterclockwise around the origin by 45 degrees. Is $A^2$ the same as the matrix you got in Question 1 the matrix you would expect for rotation of the plane counterclockwise around the origin by 180 degrees?

I understand the first one but am completely lost on how to do the second part.

1 Answers 1

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Hint:

Rotation counterclockwise by an angle $\;t\;$ is given by

$$A_t:=\begin{pmatrix}\cos t&-\sin t\\\sin t&\cos t\end{pmatrix}$$

Perhaps you should prove the above geometrically. It is rather easy and only requires very basic trigonometry.