Given a 2×22 times 22×2 matrix A=,A = begin{pmatrix}. end{pmatrix},A=, find AnA^nAn where A1=A,An=A×An1A^1 = A, A^n = A times A^{n - 1}A1=A,An=A×An1. As the result may be large, you are going to find only the remainder after division by 7. *Special Note*: The problem is intended to be easy. Feel free to think why the problem is called `2016` if you either: 1. find it hard to solve; 2. or, solved all the other problems easily.
Given a 2×22 times 22×2 matrix A=(a11a12a21a22),A = begin{pmatrix} a_{11} & a_{12} \ a_{21} & a_{22} \ end{pmatrix},A=(a11a21a12a22), find AnA^nAn where A1=A,An=A×An−1A^1 = A, A^n = A times A^{n - 1}A1=A,An=A×An−1. As the result may be large, you are going to find only the remainder after division by 7. *Special Note*: The problem is intended to be easy. Feel free to think why the problem is called `2016` if you either: 1. find it hard to solve; 2. or, solved all the other problems easily.
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