Orthogonal projection and reflection (matrices)

[Clandry]

Homework Statement

[Imgur](http://i.imgur.com/VFT1haQ.png)

Homework Equations

reflection matrix = 2*projection matrix - Identity matrix

The Attempt at a Solution

Using the above equation, I get that B is the projection matrix and E is the reflection matrix.
Can someone please verify if this is indeed the correct procedure?

 

[RUber]

Your justification for the projection matrix might need some fleshing out.
The equation for the reflection matrix justifies your choice of E if you can show that B is a projection matrix.