What is the remainder when $5 ^ {99}$ is divided by 13?

What is the value of the determinant of the inverse of the matrix $\begin{bmatrix} -4 & -5 \\ 2 & 2 \end{bmatrix} ?$

In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play at least one of the two games. How many students like to play exactly one game?
 

The system of equations 15y - 10x + 50 = 0, 2x - 3y - 5 = 0