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How do I get a matrix from a reflection?

I have the following question: $S : \Bbb{R}^2 \to \Bbb{R}^2$ is the reflection at the line $y = 2$. How do I get the matrix of $S$ at homogeneous coordinates? And to be honest, I don't get this

mathematics

mathematics

$T=-T^{*}$, show that $T+\alpha I$ is invertible.

Please don't answer the question. Just tell me if I am in the right direction. I should be able to solve this. We are given $T=-T^{*}$, show that $T+\alpha I$ is invertibe for all real alphas tha

mathematics

Is the following a reflection matrix

Suppose that $A,B \in \mathbb{R}^{n \times n}$. Let $A^2=A$ so that $A$ is a projection, $B^2=I$, and $B=2A-I$. Is it true that $B$ represents a reflection?

mathematics

mathematics

mathematics