Linear Algebra – How to Determine if a Matrix is Invertible

Question

$$\begin{bmatrix} 1235 &2344 &1234 &1990\\
2124 & 4123& 1990& 3026 \\
1230 &1234 &9095 &1230\\
1262 &2312& 2324 &3907
\end{bmatrix}$$

Clearly, its determinant is not zero and, hence, the matrix is invertible.

Is there a more elegant way to do this?

Is there a pattern among these entries?

Answer 1

Find the determinant. To make calculations easier, work modulo $2$! The diagonal is $1$'s, the rest are $0$'s. The determinant is odd, and therefore non-zero.