The Huge Matrix

Algebra Level 3

\[\begin{align} \begin{vmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 2 & 2 & 2 & 2 \\ 1 & 2 & 3 & 3 & 3 & 3 \\ 1 & 2 & 3 & 4 & 4 & 4 \\ 1 & 2 & 3 & 4 & 5 & 5 \\ 1 & 2 & 3 & 4 & 5 & 12 \end{vmatrix}\end{align}\]

Find the determinant of above matrix.

Note: Look at the last number in the matrix

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