Proving/Disproving: RQ is Tridiagonal Matrix

[kat18]

Hi, I'm having some difficulty with the following, please help.

Suppose A in R^{nxn} (n>3) is a tridiagonal matrix where Q is an orthogonal matrix and R is an upper-triangular matrix such that A=QR .

Must RQ be a tridiagonal matrix?
If yes, give a proof; otherwise, construct a counterexample.

 

[AKG]

RQ = Q^-1AQ = Q^TAQ. I don't know how much that helps, but it may be a start.