Prove that If det (A) = 1 and all entry (entries) in A is an integer, then all income in A ^ (- 1) is also an integer.

If det (A) = 1 and all entry (entries) in A is an integer, then all income in A ^ (- 1) is also an integer.

Ans:
By using the adjoint method to find the inverse of a matrix, we know that A ^ (- 1) = 1 / | A | (adj (A)) and if det (A) = 1 then, A ^ (- 1) = adj (A). The next step is to compute the adjoint matrix of cofactors and cofactor do tansposisi the matrix in which all entry (entries) in A are integers will cause cofactor searched, they also are in the form of an integer. Therefore, all proceeds in A ^ (- 1) is also an integer where A ^ (- 1) = adj (A) after adj (A) is an integer. In short, if det (A) = 1 and all entry (entries) in A is an integer, then all income in A ^ (- 1) is an integer also been proved.

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