Reflect And Transform

Geometry Level 4

$A=\frac{1}{9}\begin{bmatrix}-1 & 8 &4\\8 & -1 & 4\\4 & 4 & -7\end{bmatrix}$

What kind of a transformation of $\mathbb{R}^3$ does $A$ represent?

None of the others Orthogonal Projection onto a plane Reflection about a line Reflection about a plane Rotation through an angle

0<\theta<\pi