Verify the correctness of the matrix multiplication, $AB=C$ where,

$A=\left[\begin{array}{ccc}1& 2& 3\\ 5& 6& 7\\ 9& 10& 11\end{array}\right],B=\left[\begin{array}{ccc}5& 6& 7\\ 8& 9& 10\\ 11& 12& 13\end{array}\right],C=\left[\begin{array}{ccc}54& 60& 66\\ 158& 168& 186\\ 246& 132& 306\end{array}\right]$

$($a$).$ Demonstrate the approximation algorithm to find the minimum cost tour $(TSP)$ on graph

$($b$).$ Compare the cost of the algorithm to the optimal cost.