Is it possible to deploy to cloud a matrix entry form and when
submit button would be clicked and then an operation using entered matrix as argument would be executed?
So far I am able to deploy APIFunction[] and FormFunction[] to cloud:
CloudDeploy[APIFunction[{"x" -> "Number"}, #x^2 &], Permissions -> "Public"]
CloudDeploy[FormFunction[{"name" -> "String", "age" -> "Integer"}, 1]]
, but is there a way I could get similar results to FormFunction[], but instead of form, have a matrix input?

dispMatrixfunction that generates whatever result you want to return. – C. E. Feb 19 '16 at 10:41