I want to build a matrix, from the following set $S = \{a b , a c\}$

```
  S = {a b , a c}

```

where the terms of S represent the raw of the matrix `m` , and the element in S represent the column of the matrix `m` , then we get 

Column of m such that `c1={a,a},c2={b,0} and c3={0,c}`

raw of m such that `r1={a,b,0} and r2={a,0,c}`

building `m` from columns `m={c1,c2,c3}`
or building `m` from raw `m={r1,r2}`,
then we get 

```
m={{a, b, 0}, {a, 0, c}}

```

> 
> $m=\left( \begin{array}{ccc} a & b & 0 \\ a & 0 & c \\ \end{array}
>  \right)$
> 
> 
> 

Is this possible in practice?

In general, is this possible regardless of the terms of set?

Thanks for the help.