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