Let $\displaystyle A= \left(\begin{array}{ccc}1&0&1\\0&1&1\\0&0&0\end{ar ray}\right)$

Find non-singular matrices P,Q such that the matrix PAQ is a diagonal matrix D in which the diagonal elements are ones or zeroes, the ones coming before the zeroes,

(a) using elementary row and column operations; and

(b) by finding suitable bases of R3.

I can do (a) using pretty simple column operations to get P as the Identity Matrix and $\displaystyle Q=\left(\begin{array}{ccc}1&0&-1\\0&1&-1\\0&0&1\end{array}\right) $ which gives $\displaystyle PAQ=\left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\en d{array}\right)$

I don't really have a clue how to do part b) any help much appreciated!!