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In this article, we study the forward order laws for {1, 2, 3}and {1, 2, 4}-inverses of a product of three matrices by using the maximal and minimal ranks of the generalized Schur complement. The necessary and sufficient conditions for A1{1, 2, 3}A2{1, 2, 3}A3{1, 2, 3} ⊆ (A1A2A3){1, 2, 3} and A1{1, 2, 4}A2{1, 2, 4}A3{1, 2, 4} ⊆ (A1A2A3){1, 2, 4} are presented.

The forward order laws for {1,2,3}- and {1,2,4}-inverses of a three matrix products