$M = \begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$; invertible (det = 1)

$M = \begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$; not invertible (det = 0)

$M = \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$; invertible (det = 1)

$M = \begin{pmatrix} 2 & 1 \\ 0 & 1 \end{pmatrix}$; invertible (det = 2)