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## Homework Statement

Find the standard matrix of T

[tex]T: \mathbb{R}^2 \to \mathbb{R}^2[/tex] rotates points (about the origin) through [tex]\frac{3 \pi}{2}[/tex] radians counterclockwise

## The Attempt at a Solution

I just substitute [tex]\frac{3 \pi}{2}[/tex] into the rotation matrix and I got [tex]\begin{bmatrix}

0 & 1 \\

-1 & 0

\end{bmatrix}[/tex]

The book got this answer too, but they did something weird

They did [tex]T(\vec{e_1}) = -\vec{e_1}[/tex] and [tex]T(\vec{e_2}) = \vec{e_1}[/tex]

I don't understand how they got [tex]T(\vec{e_1}) = -\vec{e_1}[/tex]