Symmetric Matrices & Quadratic Forms · Medium problem

A quadratic form with matrix $A = \begin{pmatrix}2&0\\0&7\end{pmatrix}$ is transformed by the change of variables $\mathbf x = M\mathbf y$ with $M = \begin{pmatrix}1&1\\0&2\end{pmatrix}$, giving a new form with matrix $B = M^{T}AM$. Rather than multiplying out $B$ in full, use the fact $\det(M^TAM) = (\det M)^2\det A$ to find $\det B$.