Show that quaternion multiplication is not commutative. (That is, give an example to show that sometimes {n+ ng. ) ((Actually, a few examples are printed on the previous page.))

Show that B is the inverse of A. To show that B is the inverse of A, we need to show that AB = I = BA. -2 + AB = 21 -1 A- [3 } ] • - [ -5 -2] = B 95 -9 BA= - 2 [3 } ][ - 5 -1 95 -9 2 5-1 [52] [33 -9 95 - [ = 10 + 45 + - [₁ = 8 10 + -18+ -9 + = -1E 81-1881 5+ -9 +

Please give detailed steps. I’m really trying to understand this problem. Much appreciated!

Calculate the following commutators: (a) [O₂, O6]; (b) [O₁, O₂]. The procedure is to calculate [A, B] by expressing A(B) - B(A) in the form C.