- #1
thepatient
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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?