Question

If
A ∈ Rnxm
, knowing that and \[\exists(A ^{T}*A)^{-1}\] and
P=A∗(AT∗A)−1∗AT;
which of these states are true? Justify your answer :
a)(AT∗A)−1
is a symmetric matrix ;
b)(AT∗A)−1
is an anti-symmetric matrix;
c)P2=P;

d)P
is symmetric ;
e)P∈Rnxn