Chapter 1 - Linear Equations in Linear Algebra - Supplementary Exercises - Page 91: 22

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By Theorem 12 in Section $1.9,$ the columns of $A$ span $R^{3} .$ By Theorem 4 in Section $1.4,$ A has a pivot in each of its three rows. Because A has three columns, each column must be a pivot column. So the equation $A x=0$ has no free variables, the columns of A are linearly independent. By Theorem 12 in Section $1.9,$ the transformation is one to one.