?Please help find a mistake - Projection Matrix

[Darya]

I have translated my solution to English, if you have any questions regarding the notations - feel free to ask.
I have checked that spaces X and Y are complementary, B is a matrix that consists of basis of X and Y.
The formula for projection matrix I have deduced I saw first during my classes. I cannot understand why my solution is wrong. (P is not even symmetric)

 

[blamocur]

Why do you think that P must be symmetrical ?

 

[Darya]

Why do you think that P must be symmetrical ?

Hi! Because it's a projection matrix?

 

[Darya]

Why do you think that P must be symmetrical ?

Oh, or it doesn't have to be symmetric :0 ? x is mapped to x by this matrix and y is mapped to 0..

 

[Darya]

Why do you think that P must be symmetrical ?

Indeed it doesn't have to be if it's not orthogonal projection?‍ P=P^2 so it is indeed a projector
I guess my problem is solved! At least this way I'll remember it better. Thank you so much!