Given a linear transformation $T:P_2(R) \to P_2(R)$ defined by

$T(f(x))=f''(x)+2f'(x)-f(x)$,

where $P_2(R)$ represents the real-valued 2nd-order polynomials. Assume $M$ is the matrix representation of $T$ with respect to the ordered basis. Please find the determinant of $(M^{-1}+2I)$, where $I$ is the identity matrix with the same dimension as $M$.