# Solving for B matrix in terms of A. Can someone check my answer?

## 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?

LCKurtz
Homework Helper
Gold Member
Yes, it looks OK but is much more complicated than it needs to be. At the first step where you have ##P^{-1}A= BP^{-1}## just multiply by ##P## on the right.

Hahaaaa. That's right. Thanks. :]

I wasn't sure if you can multiply from the right too.

Ray Vickson