Question: How can i form of the matrix representation in the following exercise?

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> Given the linear maps $f$ and $g$
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> $$f\left(\begin{bmatrix}\lambda\_1\\ \lambda\_2\\ \lambda\_3\end{bmatrix}\right)=\begin{bmatrix}\lambda\_3-\lambda\_1\\\lambda\_2-\lambda\_1\end{bmatrix}\\ g\left(\begin{bmatrix}\mu\_1\\\mu\_2\end{bmatrix}\right)=\begin{bmatrix}\mu\_2-\mu\_1\\ -2\mu\_1\\ \mu\_1+\mu\_2\end{bmatrix}$$
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> find the matrix repesentation of $g\circ f$.
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Answer: 
The matrix representation of $T:\Bbb R^n\to\Bbb R^m$ (in the canonical basis) is simply the matrix $$\begin{pmatrix}T(e\_1)& T(e\_2)&\cdots &T(e\_n)\end{pmatrix}.$$

This can be easily computed in this instance.
$f$ is represented (in the standard bases) by $$M\_f= \begin{bmatrix} -1 & 0 & 1\\ -1 & 1 & 0\end{bmatrix}$$

and $g$ by 

$$M\_g= \begin{bmatrix}
-1 & 1\\
-2 & 0\\
1 & 1
\end{bmatrix}$$

Now compute $M\_g M\_f$ as matrices