Find the determinant of a solving matrix I have such ODE:
$$\frac{dy}{dt}=\begin{pmatrix}
     \sin^2t & e^{-t}   \\ 
      e^t & \cos^2t
     \end{pmatrix} y=A(t)y(t)$$
and let $M(t,1)$ be the solving matrix (a matrix whose columns generate a fundamental system of solutions), where $M(1,1)=E$. Find $\det M(-1,1)$.
I don't really know how to tackle this problem, so I would really appreciate a solution with a bit of explanation going on, but even little hints might be invaluable.
EDIT:
I was thinking that maybe I could use the fact that $A(t)=A^T(-t)$, then:
$$y'(-1)=A(-1)y(-1)=A^T(1)y(1)$$
$$A(-1)M(-1,1)=A^T(1)M(1,1)=A^T(1)E$$
$$M(-1,1)=A^T(1)EA^{-1}(-1)$$

@Max, read your book. The wronskian $W(t)=\det(M(t,1))=\exp(\int_{1}^t trace(A(u))du)$.
Here $trace(A(t))=1$ and $W(t)=\exp(t-1)$.
