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In \(M^3(C)\) consisting of all \(3\times3\) complex matrices \begin{equation} A= \begin{pmatrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33} \end{pmatrix} \end{equation} which of the following are linear functionals?
- \(\phi(A) = \text{Tr}(A) \)
- \(\phi(A)= \text{Tr}(a) + \text{Tr}(A^T)\)
- \(\phi(A) =\det (A)\)
- \(\phi(A)= A_{11}+A_{21} + A_{31} \)
- \(\phi(A) = A_{11}.\)
- \(\phi(A)= A_{12}A_{32}\)
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