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{\bf Question}

Prove that if a matrix $A$ and its inverse both have all their
elements integers, then $\det A = \pm 1$

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{\bf Answer}

If $A$ has all its entries integers then $\det A$  is an integer.

Ditto for $\det A^{-1}$ $1 = \det A \cdot A^{-1} = \det A \det
A^{-1}$

therefore $\det A = \det A^{-1} = \pm 1$


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