(a) Construct two non-zero 3×3 matrices P and Q with integer entries such that PQ=O3×3.
(b) Show by direct computation that your matrices in part (a) multiply to give the zero matrix.
(c) Determine the determinants of P and Q obtained in part (a) and comment on whether each matrix is singular or non-singular.
(d) From your example and calculations, state whether it is possible for a non-singular 3×3 matrix to have a non-zero right factor whose product with it is the zero matrix. Justify your answer clearly.