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given a n x n matrix (with n>1) "A" such that all entries are integers and A is invertible such that A^{-1} also has integer entries. Let B be another matrix with integer coefficients so that:

A+B, A+2B, A+3B, ... A+(n^2)B

Are all invertible with integer entries.

Show that,

A+kB

Is also invertible with integer enties for any integer k.

who the heck do you solve this?