- #1

JasonHathaway

- 115

- 0

## Homework Statement

Proof that (A×B) . (B×A) + (A . B)^2= A^2 . B^2

## Homework Equations

A×(B×C)=(A . C)B - (A . B)C

## The Attempt at a Solution

Assuming K=(A×B)

K . (B×A) + (A . B)^2 = A^2 . B^2

B . (A×K) + (A . B)^2 = A^2 . B^2

B . [A×(A×B)] + (A . B)^2 = A^2 . B^2

B . [(A . B)A - (A . A)B] + (A . B)(A . B) = A^2 . B^2

(A . B)(B . A) - (A . A)(B . B) + (A . B)(A . B) = A^2 . B^2