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## Homework Statement

Suppose P is invertible and A = PBP^-1. Solve for B in terms of A.

## Homework Equations

(AB)^-1 = B^-1*A^-1

## The Attempt at a Solution

multiply from the left of each side of the equation by P^-1:

P^-1 *A = BP^-1

Take the inverse of both sides:

(P^-1*A)^-1 = (BP^-1)^-1

A^-1 * P = P*B^-1

Multiply from the left of each side of the equation by P^-1:

P^-1*A^-1*P = B^-1

Take the inverse of both sides:

[P^-1(A^-1*P)]^-1 = B

B = (A^-1*P)^-1*P

B = P^-1 *A * P

Is that correct?