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Invertible Matrix over Complex Numbers

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?

keywords: matrices

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