Symmetric Matrices & Quadratic Forms · Hard problem

A dataset's design matrix is $A = \begin{pmatrix}1 & 0\\1 & 1\\0 & 1\end{pmatrix}$. The least-squares normal equations use the quadratic form $q(\mathbf x) = \mathbf x^{T}(A^{T}A)\mathbf x$. Since $A$'s columns are independent, $A^TA$ is positive definite. Compute $A^TA$ and find its SMALLER eigenvalue.