We are giving a matrix $Q=\frac{1}{9}\begin{bmatrix} -1 & 8 & 4 \\ 4 & 4 & -7 \\ 8 & -1 & 4 \end{bmatrix}$
The question askes to describe, without any further caclulation, the geometric effect of multiplying a non-zero vector by $Q$.
I have shown that $Q$ is a reflection combined by a rotation, as $Q$ is an orthogonal matrix and det($Q)=-1$. But I do not understand what multiplying $Q$ by a non-zero vector would achieve.