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. Motivated by the equivalent conditions for the inclusions An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} ⊆ (A1A2 · · ·An){1, 2, i} (i = 3, 4) presented in [B. Zheng and Z. Xiong. The reverse order laws for {1,2,3}and {1,2,4}-inverses of multiple matrix products. Linear Multilinear Algebra, 58:765–782, 2010.], we show that for i ∈ {3, 4}, An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} = (A1A2 · · ·An){1, 2, i} is equivalent to An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} ⊆ (A1A2 · · ·An){1, 2, i}.

A note on the reverse order laws for {1, 2, 3}- and {1, 2, 4}-inverses of multiple matrix products