Defining a funtion on the set of matrics over real numbers

Question

Problem:

Each of the following expressions defines a function D on the set of matrices over the field of real numbers. In which of these cases is D a 3-linear function? Justify your conclusions.

a) D (A) = A₁₁+A₂₂+A₃₃

b)D (A) = A₁₁A₂₂A₃₃

Recall: Let K be a commutative ring with identity, n a positive integer, and let D be a function which assigns to each matrix A over K a scalar in K. We say that D is n-linear if for each , D is a linear function of the ith row when the other
(n-1) rows are held fixed.