For which matrix does an inverse exist?
(2412)\begin{pmatrix} 2 & 4 \\ 1 & 2 \end{pmatrix}(2142)
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)
(0000)\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}(0000)
(1224)\begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix}(1224)