# Determinant of GCD Matrix

Let $$A$$ be an 16 by 16 matrix, with entries $$a_{i,j} = \gcd(i, j )$$ for $$1 \leq i, j \leq 16$$. Calculate the last 3 digits of $$\det (A)$$.

Details and assumptions

$$\det(A)$$ refers to the determinant of matrix $$A$$.

$$\gcd(i,j)$$ refers to the greatest common divisor of $$i$$ and $$j$$.

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