Let 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 Q=\left(\begin{array}{ccc}1&0&-1\\0&1&-1\\0&0&1\end{array}\right) which gives 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!!