Question $2.$ Let $A$ be the adjacency matrix of a complete graph $K_4.$

$($a$)$ Write down matrix $A.$

$($b$)$ How many possible walks with length $2$ are there from a $($any$)$ node to itself $($e$.$g$.,$ from Node $2$ to itself$)$

$($c$)$ How many possible walks with length $3$ are there from a $($any$)$ node to the other node $($e$.$g$.,$ from Node $2$

to Node $3$ or Node $1$ to Node $4)$