In this paper, we prove that the generalized matrix algebra G = \left[ A M N B \right] is a zero triple product (resp. zero Jordan triple product) determined if and only if A and B are zero triple products (resp. zero Jordan triple products) determined under certain conditions. Then the main results are applied to triangular algebras and full matrix algebras.

In this paper, we prove that the generalized matrix algebra G = \left[ A M N B \right] is a zero triple product (resp. zero Jordan triple product) determined if and only if A and B are zero triple products (resp. zero Jordan triple products) determined under certain conditions. Then the main results are applied to triangular algebras and full matrix algebras.