What am I doing wrong in attempting to find the least squares solution of the system Ax = b? I am attempting to find the least-squares solution x* of the system Ax = b, where 
$$
        A = \begin{bmatrix}
        1 & 2 & 3 \\
        4 & 5 & 6 \\
        7 & 8 & 9 \\
        \end{bmatrix}
$$
and
$$
        B = \begin{bmatrix}
        1  \\
        0  \\
        0  \\
        \end{bmatrix}
$$
I'm trying to solve for x* using the formula $$x^* = (A^TA)^{-1} A^Tb $$
I am getting stuck after I calculate  $$(A^TA)=
        \begin{bmatrix}
        66 & 78 & 90 \\
        78 & 93 & 108 \\
        90 & 108 & 126 \\
        \end{bmatrix}
$$
because I am getting an error when I attempt to calculate the inverse of this matrix in my calculator. What am I missing?

The determinant of $A$ is $0$, hence it is not invertible.
