How to show that $$A=\begin{pmatrix}1233&2344&1324&3456\\ 2342&11233&1432&13256\\234132&32432&1234567&43254\\423412&42354&452356&13245\end{pmatrix}$$ is invertible ? I could compute the determinant, but it's very very long...
2026-04-05 17:57:55.1775411875
Show a matrix is invertible
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If you take the coefficients modulo 2, you see that there is only $1$ on the diagonal and $0$ elsewhere. Therefore $$\det A\equiv 1\pmod 2,$$ and thus $\det A$ is odd. Therefore $\det A\neq 0$ and thus $A$ is invertible.