A =ailAii+a12A12+a13A13+��� +ainAin) (A) � A = lk + a2kA2k +a3kA3k +��� +ankAnk This theory enables the evaluation of a determinant by successive reduction of the orders of the determinants involved.
From the theorem given above for the expansion of a determinant as a sum of products of pairs of corresponding determinants it will be plain that the product of A= (a ll, a22, ��� ann) and D = (b21, b 22, b nn ) may be written as a determinant of order 2n, viz.
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