Okay, well what haveyoudone? Do you know how to find the eigenvalues? For 2 by 2 matrices it is just solving a quadratic equation.

A matrix is singular if and only if it has at least one 0 eigenvalue.

An n by n matrix can be diagonalized if and only if it has n independent eigen[b]vectors/b] in which case the matrix is the matrix having those eigenvectors as columns.