Why is this rotation "incorrect"? I've been trying to use the following formula for the rotation of a point around the origin:
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
$$
Now, I'm trying to apply this formula to the coordinate $(5,3)$ and rotating it $90$ degrees clockwise, and I ended up with the following result:
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{90} & -\sin{90} \\
\sin{90} & \cos{90}
\end{bmatrix}
\begin{bmatrix}
5 \\ 3
\end{bmatrix} 
\\
=
\begin{bmatrix}
0 & -1 \\
1 & 0
\end{bmatrix}
\begin{bmatrix}
5 \\ 3
\end{bmatrix} 
\\
=
\begin{bmatrix}
0(5) -1(3) \\
1(5) + 0(3)
\end{bmatrix} \\
=
\begin{bmatrix}
-3 \\ 5
\end{bmatrix}
$$
I ended up with the rotated coordinates $(-3,5)$. Unfortunately, this was wrong. Can anyone tell me what I'm doing wrong, and how I can do it correctly? I tried this method on other coordinate points, and all of them were wrong as well.

It is correct. What makes one think that it is wrong? You mean the convention that CCW is positive?
EDIT1:
What I meant is with Clockwise rotation I obtain $(-3,5)$ by matrix multiplication and Counterclockwise rotation gives  $(3,-5)$ for a diametrically opposite point. So only association with sign convention of rotation could be the source of error.
