3.8 Show that tr(ASA') - E, a Sa; as in (3.65). a Sa, a, Say . . . a Sax A,Sal ASa . .. ASak S. = (3.63) a Sa1 a Saz . .. aSak a (Saj, Say, . . . Sax) a; (Saj, Saz, . . . Sax) = a, (Sal, Sa2, . .. Sax) (Sal, Saz, . ...Sax) [by (2.47)] S(a1 , a2, . .., ax) [by (2.48) ] = ASA'. (3.64) Note that by (3.63) and (3.64), we have tr(ASA') = ) a Sai. (3.65) i=1