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I am studying for exam and something does not make sense anymore:

looking at projection matrix, how come P=P

P

= A(A

= P

but then they also say that cancelations (like distributing inverse operation and having AA

Could someone "unconfuse" me please?

EDIT: might as well ask this:

find matrix of projection p on plane x+y+2z = 0

my attempt: I know that the normal vector is (1, 1, 2) and then... not sure where to go with that...

looking at projection matrix, how come P=P

^{2}whereP

^{2}= A(A^{T}A)^{-1}A^{T}A(A^{T}A)^{-1}A^{T}= A(A

^{T}A)^{-1}A^{T}= P

but then they also say that cancelations (like distributing inverse operation and having AA

^{-1}= I type things) are possible only if A is invertible, so does that mean that A^{T}A is invertible?Could someone "unconfuse" me please?

EDIT: might as well ask this:

find matrix of projection p on plane x+y+2z = 0

my attempt: I know that the normal vector is (1, 1, 2) and then... not sure where to go with that...

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