Answer
See answer below
Work Step by Step
Let A be an $n \times n$ invertible matrix.
The least squares solution is given by $x_0=(A^TA)^{-1}A^Tb$
Since $A$ is an invertible matrix, $A^T$ then will be:
$A^T(A^T)^{-1}=(A^T)^{-1}A^T=I$
We can obtain:
$x_0=(A^TA)^{-1}A^Tb \\
=A^{-1}(A^T)^{-1}A^Tb \\
=A^{-1}b$
Hence, $x_0=x=A^{-1}b$
t the
It is proved that the unique solution to the linear system $Ax = b$, is also the least squares solution for this system.
