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Find the number of matrices whose determinant is a multiple of 13 where the first column is not a multiple of 13 but the second column is a multiple of the first modulo 13.

Here's what I have done:

The number of combinations when the first column is not multiple of 13 is $(26^2-2^2) = 2^2×(13^2-1)$ The number of combinations when the second column is multiple of 13 is $2^2$ Thus, the total combinations: $2^4 × (13^2 - 1)$

The solution given is: $2^4 × (13^2 - 1) x 13$

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