Prove the following using a direct proof. Your proof should be expressed in com-plete English sentences.Ifa,b, andcare integers such thatbis a multiple ofa3andcis a multiple ofb2,thencis a multiple ofa6

The transformation (x, y) ⇒ (y, -x) represents rotation 90° clockwise about the origin.

It could also be accomplished by
  • reflection across the line y=x, and
  • reflection across the x-axis

or
  • reflection across the line y=-x, and
  • reflection across the y-axis

or
  • reflection across the y-axis
  • reflection across the line y=x, and

or
  • reflection across the x-axis
  • reflection across the line y=-x, and.