Determine 3 × 3 invertible matrices $P$ and $Q$, such that $PAQ = B$, where
$A = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 &1 \\ 0 &1 &0 \end{pmatrix}, B = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 &0 \\ 0 &0 &0 \end{pmatrix}$
I wanted to use diagonalization but diagonal entries of $B$ aren't eigenvalues of $A$ or their multiples. I then thought about row operations to get from $A$ to $B$ but didn't know how. This might be simple linear algebra question but I am really stuck. Could anyone shed light on it? Many thanks.
Solved.