Consider the standard basis (e1, e2, e3) for R 3 . There are six permutations of the vectors in the standard basis. These six permutations include one "identity" permutation (defined by ei ei for each i), three "transpositions" (e.g., e1 e2, e2 e1, e3 e3), and two "3-cycles" (e.g., e1 e2 e3 e1). Write down the matrix associated to each of the six permutations of the standard basis.