- #1
barbiemathgurl
- 12
- 0
i just can't figure this out.
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?
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?