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Linearly Independent Vectors

(a) Show that [a × b, b × c, c × a] = [a, b, c]^2
(b) If a, b, c are three linearly independent vectors show that the vectors a × b, b × c,
c × a are also linearly independent.
(c) For any vector x, we express it in terms of these latter vectors
x = λa × b + µb × c + νc × a, λ, µ, ν ∈ R,
Find λ, µ and ν in terms of a, b, c and x.

I have managed parts (a) and (B) but I'm struggling on (c). I have seen a method for when the vectors are NOT linearly independent but I have just proved that if a,b,c are linearly independent then so are axb, bxc, cxa