Let P and Q be permutation matrices of the same size as a square matrix . Prove that = with = PAQ, = QTx, and = Pb is just another way of recording the system Ax = b and that = with = PAQ, =...

Let P and Q be permutation matrices of the same size as a square matrix
. Prove that

=

with

= PAQ,

= Q^Tx, and

= Pb is just another way of recording the system Ax = b and that

=

with

= PAQ,

= yP^T,

= cQ, is just another way of recording the system yA = c.