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## Homework Statement

Hi. I need to prove that [b x c, c x a, a x b] = [a, b, c]

^{2}for any three vectors a, b and c.

Note that [a, b, c] = a(b x c)

## Homework Equations

I tried using the identify (a x b) x c = (a.c)b - (a.b)c

## The Attempt at a Solution

Using the above identity I got [b x c, c x a, a x b] = (b x c){(c x a) x (a x b)} = (b x c){(a(a x b)a - (ca)(a x b)}. I'm not sure where to go from here or if it's the correct approach at all

Thanks for any help!