Answer
True
Work Step by Step
The projection matrix is: $P = A(A^T A)^{−1}A^T$
If A is an invertible $m×n$ matrix then $A^T(A^T)^{-1}=I_n$
which is followed by the formula $A^{-1}=A^{-1}A=I_n$
Thus: $P = A(A^T A)^{−1}A^T=AA^{-1}A^T(A^T)^{-1}=I_n$
The statement is true
