Let X, Y, Z be Banach spaces. For the identity operator I on X and a quotient operator Q: Z → Y, in this paper we investigate conditions under which I ⊗ Q and Q ⊗ I are again quotient operators on the respective tensor product spaces. Let J ⊂ X be a closed subspace. For the quotient injective tensor product space (X ˆ⊗ɛ Y )/(J ˆ⊗ɛ Y ), we consider several geometric properties of Banach space X and J under which this quotient space is isometric to (X/J) ˆ⊗ɛ Y . We show that for a L1-predual space X and for a special type of M-ideal J ⊂ X, the spaces under consideration are isometric. © 2019 American Mathematical Society.