Matrix Transformation Problem

Question

The transformation matrix $P$ represents a $90^\circ$ anticlockwise
rotation about the origin.

Describe fully the single transformation represented by the matrix
$P^3$

From my working, $P$ would equate to

\begin{equation*}
P =
\begin{bmatrix}
0 & -1 \\
1 & 0
\end{bmatrix}
\end{equation*}

Now to find the transformation shown by $P^3$, would I have to cube the matrix or is there something that I'm missing here?

Thanks in advance.

Answer 1

You can compute $P^3$ or use the fact that if $P$ rotates vectors through an angle $\theta$, then $P^n$ rotates vectors through the angle $n\theta$.