Originally Posted by

**AlmightyMidget** So, I'm given this question that I am REALLY stuck on, I honestly have no idea where to begin, it's got me absolutely stumped and none of the information I have on hand helps me out (Unless I'm overlooking something simple). Anyway, the question is:

The five numbers 21,375 38,798 34,162 40,223 and 79,154 are all divisible by 19. Prove that the determinant of the matrix:

$\displaystyle \begin{pmatrix}2&1&3&7&5\\3&8&7&9&8\\3&4&1&6&2\\4& 0&2&2&3\\7&9&1&5&4\\\end{pmatrix}$

is also divisible by 19

Any help would be appreciated