Find the determinant of the linear transformation $$T(M) = \left[\begin{array}{cc} 1 &2\cr 2 &-4 \end{array}\right] M + M \left[\begin{array}{cc} 1 &2\cr 2 &-4 \end{array}\right]$$ from the space $V$ of symmetric $2\times 2$ matrices to $V$.

$\det =$