Chapter 2.4, Problem 42E

True or False? In Exercises $\mathit{ }41$ and $\mathit{ }42$, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) The zero matrix is an elementary matrix.

(b) A square matrix is nonsingular when it an be written as the product ofelementary matrices.

(c) $A\mathbf{x}=O$ has only the trivial solution if and only if $A\mathbf{x}=\mathbf{b}$ has a unique solution for every $n\times 1$ column matrix $\mathbf{b}$.