I have no idea how to solve it. Please help me out! Thank you!
Let $\alpha$ be a plane in $\mathbb{R}^3$ passing through the origin, suppose $\alpha$ is given by the equation $ax + by + cz = 0.$ Reflection in $\alpha$ is a linear transformation $T$ of $\mathbb{R}^3$.
Find a matrix representation of $T$ with respect to the standard basis of $\mathbb{R}^3$ (bear in mind that reflection does not change length).
Hint: find $T$ as a composition of a transformation, which maps the normal of $\alpha$ to one of the coordinate axes, and a reflection in the corresponding coordinate plane.