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Change of basis matrix

Here is the question I have been given:

ma553 4.png

I do not know how to express the image in terms of x and y, but here's my answer to the second part:

Mϵϵ(ψ)=(45911) M_{\epsilon}^{\epsilon}(\psi)= \begin{pmatrix} 4 & 5 \\9 & 11 \end{pmatrix}

Mβϵ(id)=(351017) M_{\beta}^{\epsilon}(id)= \begin{pmatrix} 3 & 5 \\10 & 17 \end{pmatrix}

Mϵβ(id)=Mβϵ(ψ)−1=(351017)−1=(17−5−103) M_{\epsilon}^{\beta}(id)= M_{\beta}^{\epsilon}(\psi)^{-1}= \begin{pmatrix} 3 & 5 \\10 & 17 \end{pmatrix}^{-1} = \begin{pmatrix} 17 & -5 \\-10 & 3 \end{pmatrix}

So: Mββ(ψ)=Mϵβ(id).Mϵϵ(ψ).Mβϵ(id)=(17−5−103).(45911).(351017) M_{\beta}^{\beta}(\psi) = M_{\epsilon}^{\beta}(id). M_{\epsilon}^{\epsilon}(\psi). M_{\beta}^{\epsilon}(id) = \begin{pmatrix} 17 & -5 \\-10 & 3 \end{pmatrix} . \begin{pmatrix} 4 & 5 \\9 & 11 \end{pmatrix} . \begin{pmatrix} 3 & 5 \\10 & 17 \end{pmatrix}

So: Mββ(ψ)=(369625−209−384) M_{\beta}^{\beta}(\psi)= \begin{pmatrix} 369 & 625 \\-209 & -384 \end{pmatrix}

Is my method here correct or have I gone wrong somehow? Thank you for any help!
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