Answer
Applying Th.4 from Chapter 1, we find that there are pivots in each row of A.
Since A is a square matrix, there are no free variables, so
$A\mathrm{x} =\mathrm{b}$ has only one solution.
Work Step by Step
Applying Th.4 from section 1-4, we have
$\mathrm{a}.\quad A\mathrm{x} =\mathrm{b}$ has a solution for each $\mathrm{b}.$
Then,
$\mathrm{d}.\quad A$ has a pivot in each row.
Since A is n$\times$n, a square matrix,
there are no free variables in $A\mathrm{x} =\mathrm{b}$,
so there is only one solution to $A\mathrm{x} =\mathrm{b}$.
