a) An invertible matrix A with integer entries is said to be unimodular if A–1 also has integer entries. Show that if A is a square matrix with integer entries such that det(A) = ±1, then A is a unimodular matrix.
b) Prove the converse of the result in part (a); i.e., prove that if A is a unimodular matrix, then det(A) = ±1.
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