likelihood, covariance matrix, matrix trace property

4. Assume X1, ..., Xn are random sample from a multivariate normal population with mean / and covariance matrix E. We can derive the multivariate maximum likelihood 1 n L ( M, E) = (2 7 ) np / 2 )|n/2 expl - ? _ ( X ( i) - M) TE- 1(X(i) - M) } i=1 Please show that L ( M, E) = 1 (27 ) np/2 En/2 expl-2 tr[EEt(X(i) - X) (X(i) - X) ] + n(X - M) E-' (X - M) ]]}