Prove that if p is a prime in Z that can be written in the form a2 + b2,then a + bi is irreducible in Z[i]. Find three primes that have thisproperty and the corresponding irreducibles

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A: As per the guidelines I am answering only one question at a time. 1] P=12-34-1-23-41-23-412-3-4

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Q: Evaluate the determinant of the matrix -3 4 P = -1 1 1 2-3 -2 -2 3 -4 -2 3 -3-4 2

A: We have to find the determinant of  P=12-34-1-23-41-23-412-3-4 Determinant of a matrix is the…

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