1. The problem statement, all variables and given/known data Show that the members of the Lie algebra of SO(n) are anti-symmetric nxn matrices. To start, assume that the nxn orthogonal matrix R which is an element of SO(n) depends on a single parameter t. Then differentiate the expression: R.RT= I with respect to the parameter t, keeping in mind that I is a constant matrix. Then you must consider that the element M of the Lie algebra is defined as: M = (dR/dt) t=0 And that R(0) is the identity matrix. 2. Relevant equations (A.B)T = B T.A T 3. The attempt at a solution d/dt[R(t).RT(t)] = 0 I was introduced to linear algebra and group theory very recently and am having trouble doing any of the proofs that I am assigned for homework. I feel that this problem is probably easy, but it is surely not coming to me easily at all. . . Please help!