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Consider the 3x3 rotation transformation matrix [ Ro] = tr₁ r2-sr3 tr₁r3+ sr2 trí tế tr2r1+sr3 tr + tr₂r3-sr 1 tr3 r1-sr2 tr3 r2 + sr₁ tr3² + c where c = cos 0, t = 1 - cos 0, and s = sin e Assume that [Ro] = [a₁ a2 a3 ] where a₁, a2, and a3 are the images of the unit vectors e₁,e2, e3 under the rotation transformation. The inverse rotation [ Ro ] -¹ of [ Ro ] is equal to trí t tr₂ r1 + sr3 tr3 r₁ - Sr2 tr₁ r2-sr3 trẻ to tr3 r2 + sr 1 tr₁ r3+ sr2 tr₂ r3 - s r₁ tr3² + c The inverse rotation [Ro ] ¹ of [Ro] is equal to [ Ro] T The inverse rotation [Ro]¹ of [Ro] can be constructed using the same axis r and then replacing the angle 8 with -0, and then using cos(-0) = cos(0) = c, 1- cos(-0) = 1 - cos(0) = t, and sin(-0) = -sin(0) = -s -1 The inverse rotation [Ro ] ¹ of [ Ro] can be constructed using the opposite axis -r and the same angle 0