Find the diagonal matrix when transformation and conversion matrices are known

Question

I am stuck with finding the diagonal matrix for eigenvalues.
Given the matrix T =
\begin{bmatrix}6&-1\\2&3\end{bmatrix} and change of basis matrix C= (whose columns are eigenvectors of T)
\begin{bmatrix}1&1\\1&2\end{bmatrix}
How can I calculate the diagonal matrix D = C$^{-1}$TC?

Answer 1

My answer before the question was edited: $$ \begin{pmatrix} 6 & 2 \\ 1 & 3 \\ \end{pmatrix} \begin{pmatrix} 1 \\ 1 \\ \end{pmatrix}=\begin{pmatrix} 8 \\ 4 \\ \end{pmatrix}, $$ but if \begin{pmatrix} 1 \\ 1 \\ \end{pmatrix} were an eigenvector then the result would be \begin{pmatrix} \lambda \\ \lambda \\ \end{pmatrix}.

My answer after the question was edited:

Now that you have the matrix correct, it works:

$$ \begin{pmatrix} 2 & -1 \\ -1 & 1 \\ \end{pmatrix} \begin{pmatrix} 6 & -1 \\ 2 & 3 \\ \end{pmatrix} \begin{pmatrix} 1 & 1 \\ 1 & 2 \\ \end{pmatrix}=\begin{pmatrix} 5 & 0 \\ 0 & 4 \\ \end{pmatrix}$$ is diagonal. The correct inverse is $$\begin{pmatrix} 1 & 1 \\ 1 & 2 \\ \end{pmatrix}^{-1}=\begin{pmatrix} 2 & -1 \\ \color{red}-1 & 1 \\ \end{pmatrix}$$