and that of a matrix product C= AnxkBkxT AB [Ab1 Ab2 Abr a1 a a,B a2B Two cases frequently encountered are of the form A A A A AlA 0 0A22A22 4.2 Determinants of partitioned matrices A 0A22 A A 1A2||A1-A12A12A21 1A1|·|A2-A21A1A12|and that of a matrix product C = An×kBk×T C = AB = A b1 b2 . . . bT = [Ab1 Ab2 AbT] =         a ′ 1 a ′ 2 . . . a ′ n         B =         a ′ 1B a ′ 2B . . . a ′ nB         . Two cases frequently encountered are of the form  A1 A2 ′  A1 A2  = A′ 1 A′ 2  A1 A2  = A′ 1A1 + A′ 2A2 , and  A11 0 0 A22 ′  A11 0 0 A22  =  A′ 11A11 0 0 A′ 22A22  . 4.2 Determinants of Partitioned Matrices (a).     A11 0 0 A22     = |A11| · |A22|. (b).     A11 A12 A21 A22     = |A22| · |A11 − A12A−1 12 A21| = |A11| · |A22 − A21A−1 11 A12|. 16