Prove that if $A$ is a square matrix with integer entries and $\det(A)=\pm 1$, then the inverse of $A$ contains all integer entries.
[Math] Prove the inverse of an integer matrix has only integer entries
linear algebramatrices
linear algebramatrices
Prove that if $A$ is a square matrix with integer entries and $\det(A)=\pm 1$, then the inverse of $A$ contains all integer entries.
Best Answer
Hint: Consider the inverse written in terms of the adjugate matrix.