Determine if the matrix $A$ below is diagonalizable. If the matrix is diagonalizable, then find a diagonal matrix $D$ that is similar to $A$, and provide the invertible matrix $S$ that performs the similarity transformation. You should use your calculator to find the eigenvalues of the matrix, but try only using the row-reducing function of your calculator to assist with finding eigenvectors. \begin{equation*} A= \begin{bmatrix} 1 & 9 & 9 & 24 \\ -3 & -27 & -29 & -68 \\ 1 & 11 & 13 & 26 \\ 1 & 7 & 7 & 18 \end{bmatrix} \end{equation*}