(a) Five teams took part in a competition in which each team played each of the other \(4\) teams. The following table represents the results after all the matches had been played.

Points in the competition were awarded to the teams as follows:

\(4\text{ for each match won},\qquad 2\text{ for each match drawn},\qquad 0\text{ for each match lost}.\)

(i) Write down two matrices whose product under matrix multiplication will give the total number of points awarded to each team.

(ii) Evaluate the matrix product from part (i) and hence state which team was awarded the most points.

(b) It is given that

\(A=\begin{pmatrix}1&-1\\2&4\end{pmatrix},\qquad B=\begin{pmatrix}5&0\\1&-2\end{pmatrix}.\)

(i) Find \(A^{-1}\).

(ii) Hence find the matrix \(C\) such that \(AC=B\).