Exercises on determinants and linear systems

1. Find the determinants: .
2. If A and B are matrices of the same order and det(A)=2 and det(A)=3, find det(A²B^-1).
3. Calculate the inverse: .
4. Use Cramer's rule to solve the system: .
5. Given , find the values of k for which det(A)=0. Solve the system .
6. Using Rouchè-Capelli's theorem solve the system: , where s and t are real numbers.
7. Find the values of t for which the matrix is invertible.
8. Find the values of t for which the matrix is invertible.