Let A be a square n x n matrix over C[X] and write A = [pjk (X)] .
For any z∈C( z being a complex variable) let A(z) := [pj k (z)] , that is a
square n x n matrix over C.
Show that matrix A is invertible if and only if matrix A(z) is invertible for all
z from C.
Will it be still valid if we change complex numbers into set of real?
An Invertible Matrix over Complex Numbers is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.