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A in M2(prime), A=B^2 and det(B)=p^2

Source: VJIMC 2012 1.2

May 31, 2021
matrixlinear algebra

Problem Statement

Determine all 2×22\times2 integer matrices AA having the following properties:
1.1. the entries of AA are (positive) prime numbers, 2.2. there exists a 2×22\times2 integer matrix BB such that A=B2A=B^2 and the determinant of BB is the square of a prime number.
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