It's supposed to be simple but I'm struggling with that.
Let A, B ∈ Mn(F). Prove or disprove: If a function T: Mn(F) → F is linear and multi-linear, then it is the zero function.
First, it looks like proof. I'm trying to use the definition of multi-linear which is using one matrix, two scalars, and two general rows, while to show linearity you must use two metrics with two scalars, (for example in a linear map) so I don't know how to continue (of course the obvious answer will be to use two metrics and to show the definition of the multi-linear, but I don't how, and I'm sure it is true)