Solution: To prove: If A be a square matrix with integer entries, that is aijϵZ for all , i j , then A has an inverse with integer entries if and only if ( ) = ± det A 1 Proof: Let’s assume a system of linear equations given by: = Ax b where matrix A has integer values and also assume that b is integer. Now, by Cramer’s rule: = ……………………[ ] xi detAidetA 1 Where, detAi is the determinant of the matrix
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