Number of matrices n x n with n^2 different elements which have that same characteristic polynomial

[Artur]

Dear Seqfans,
I'm asking: How many different matrices n x n with n^2 different elements  
occured which have that same characteristic polynomial
We have to count all permutations n^2 elements in n x n matrix and count  
only these permutations
which don't changed starting polynomial
for 2 x 2 case
we have 4 matrices X^2-(a+d)X+ad-bc
a b   a c   d c   d b
c d   b d   b a   c a

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ARTUR