Recall that P is a projection matrix if and only if PT=P and P2=P. Also, recall that R is a reflection matrix if and only if RT=R and R2=I. Finally, recall that A is an orthogonal matrix if and only if AAT=I=ATA.
Let P be a projection matrix. Determine whether each of the following statements is true or false.
1. If is an eigenvalue for P, then =0 or =1.

2. −1 is an eigenvalue for P.

3. det(P)=0 or det(P)=1.

4. −P is a projection matrix.

5. P2=I

6. P is a reflection matrix.

Question

Recall that P is a projection matrix if and only if PT=P and P2=P. Also, recall that R is a reflection matrix if and only if RT=R and R2=I. Finally, recall that A is an orthogonal matrix if and only if AAT=I=ATA. 
Let P be a projection matrix. Determine whether each of the following statements is true or false.
  1. If  is an eigenvalue for P, then =0 or =1.

  2. −1 is an eigenvalue for P.

  3. det(P)=0 or det(P)=1.

  4. −P is a projection matrix.

  5. P2=I

  6. P is a reflection matrix.