Let L: M(nn) ---> R1 be defined by L(A) = a11 a22 ... ann, fpr an nxn matrix A = [aij]. Is L a linear transformation

This is what I did:
L(u+v) = L(u) + L(v)

I used a matrix with a = 11 b = 1,2 etc for a 2x2 matrix. (for u)
for V i used a matrix 11= x 12=y 21= z 22= r

For L(U)+L(v) i got AD + XR
for L(U+V) i got (a+x)(d+r)

this shows that L is not a linear transformation if I am not mistaken.