Answer
By Th. 4 of chapter 1,
if the statement
"(a) the equation $A\mathrm{x}=\mathrm{b}$ has a solution for each $\mathrm{b}$ in $\mathrm{R}^{n}$" is true,
then the statement
"(d) $A$ has a pivot position in each row" is also true.
The diagonal of a reduced echelon form of A will contain the pivots.
A is therefore, row equivalent to $I_{n}.$
By Th.7, A is invertible.
Work Step by Step
The answer contains the explanation, as asked.
