(i) Consider the vectors x, y, z in R and the expression xx (yxz) +z x...

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(i) Consider the vectors x, y, z in R and the expression xx (yxz) +z x (xxy) where denotes the vector product. How can this expression be simplified? (ii) Let A, B, C be n x n matrices over C. Let [A, B] := AB - BA be the commutator. How can the expression [A, [B, C]]+[C, [A, B]] be simplified? (i) Consider the vectors x, y, z in R and the expression xx (yxz) +z x (xxy) where denotes the vector product. How can this expression be simplified? (ii) Let A, B, C be n x n matrices over C. Let [A, B] := AB - BA be the commutator. How can the expression [A, [B, C]]+[C, [A, B]] be simplified?