In this problem, we will show that the concept of non-singularity of a matrix is equivalent to the concept of invertibility.
That is, we will prove that:
(a) Show that if $A$ is invertible, then $A$ is nonsingular.
(b) Let $A, B, C$ be $n\times n$ matrices such that $AB=C$.
Prove that if either $A$ or $B$ is singular, then so is $C$.
(c) Show that if $A$ is nonsingular, then $A$ is invertible.Add to solve later