Answer:
a) Observe that
[tex]G=\left[\begin{array}{ccc}2&6\\4&0\end{array}\right] =2\left[\begin{array}{ccc}1&3\\2&0\end{array}\right] =2F[/tex]
Then, [tex]FG=F(2F)=2FF, \text{ and } GF=(2F)F=2FF[/tex]
b) The zero matrix satisfies that for every matrix B such that the product is well defined, [tex]0B=0=B0.[/tex]
Since the matrix G is the zero matrix then [tex]FG=F0=0F=GF[/tex]
c) The identity(Id) matrix satisfies that for  that for every matrix B such that the product is well defined Id*B=B=B*Id. Observe that G is the identity matrix, then FG=F*Id=F=Id*F=GF
d) Observe that
[tex]G=\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right] =3\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =3Id[/tex].
Then [tex]GF=3Id*F=3F\\FG=F(3Id)=3F*Id=3F[/tex]
