# Solution: 2012-6 Matrix modulo p

Let p be a prime number and let n be a positive integer. Let $$A=\left( \binom{i+j-2}{i-1}\right)_{1\le i\le p^n, 1\le j\le p^n}$$ be a $$p^n \times p^n$$ matrix. Prove that $$A^3 \equiv I \pmod p$$, where I is the $$p^n \times p^n$$ identity matrix.

The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!

Here is his Solution of Problem 2012-6.

Alternative solutions were submitted by 서기원 (수리과학과 2009학번, +3), 이명재 (2012학번, +2).

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