Consider the fact that $25875, 46552, 41354, 48691, 95818$ are all divisible by $23$. Use this fact to determine if \begin{vmatrix} 2 &5 &8 &7 &5 \\ 4 &6 &5 &5 &2 \\ 4 &1 &3 &5 &4 \\ 4 &8 &6 &9 &1 \\ 9 &5 &8 &1 &8 \end{vmatrix} is divisible by 23 or not, without directly evaluating the determinant.
2026-04-25 02:31:04.1777084264
Determine a determinant is divisible by 23 or not
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A determinant of a matrix can be looked at as an (antisymmetric) multilinear function on the rows of that matrix. So:
$\det(23r_1,r_2,r_3,r_4,r_5)=23\det(r_1,r_2,r_3,r_4.r_5)$