Answer:
See Explanation
Step-by-step explanation:
(a)For matrices A and C, given that: [tex]CA=I_n[/tex].
We want to show that Ax=0 has only the trivial solution
If Ax=0
Multiply both sides by C
[tex]C(Ax)=C \times 0\\\implies (CA)x=0$ (Recall: CA=I_n)\\\implies I_nx=0 $ (Since I_n$ is the n\times n$ identity matrix)\\\implies x=0[/tex]
This means that the system has only the trivial solution.
(b)If the system has more columns than rows, a free variable would occur when a column does not have a pivot. This would lead to a non-trivial solution.
