The domain space of the following functions is the space of n n real matrices A.

Question:

The domain space of the following functions is the space of n × n real matrices A. Which are linear? What is the target space in each case?
(a) L[A] = 3A
(b) L[A] = I - A
(c) L[A] = AT
(d) L[A] = A-l
(e) L[A] = detA
(f) L[A] = tr A
(g) L[A] = diag A, i.e., the diagonal entries of A
(h) L[A] = A v where v ∈ Rn is a fixed vector
(i) L[A] = vT A v where v e Rn is a fixed vector