Matrices and linear systems

Compute determinant of $\left[ \begin{smallmatrix} 1 & 1 & 1 \\ 2 & 3 & -5 \\ 1 & -1 & 0 \end{smallmatrix}\right]$

Find $t$ such that $\left[ \begin{smallmatrix} 1 & t \\ -1 & 2 \end{smallmatrix}\right]$ is not invertible.

Solve $\left[ \begin{smallmatrix} 1 & 1 \\ 1 & -1 \end{smallmatrix}\right] \vec{x} = \left[ \begin{smallmatrix} 10 \\ 20 \end{smallmatrix}\right]$.

Suppose $a, b, c$ are nonzero numbers. Let $M=\left[ \begin{smallmatrix} a & 0 \\ 0 & b \end{smallmatrix}\right]$, $N=\left[ \begin{smallmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{smallmatrix}\right]$.

1. Compute $M^{-1}$.
2. Compute $N^{-1}$.