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pbwf

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## Homework Statement

A is an nxn invertible matrix. Show that

P

_{A-1}(x) = ([tex]\frac{(-x)^n}{det(A)}[/tex]) *P

_{A}(1/X)

## Homework Equations

det(AB) = det(A)det(B)

## The Attempt at a Solution

Ok from what I understand this is the proof for the characteristic polynomial for the inverse of a matrix. The professor said that we need to use somehow the equation above.

I also understand that the equation is usually of the form det(A-[tex]\lambda[/tex]I) = 0, but I cannot see how to form this given the final equation which we need to produce.