Suppose I have a system of difference equations:
$Y_{t+1} = AY_t + C$,
where A is a 2x2 matrix, $Y_{t+1}$ and $Y_t$ are $2$ x $1$ matrices. Now generally, I would find eigenvalues using the characteristic polynomial, and if they both lay inside the unit circle I have a sink. This gets tedious if I have variables in A, instead of numbers. Could I use some property of determinants to reach the same conclusion?