Solution 3c 15

Suppose $A$ is an $n$ -by- $n$ matrix and $1 \le j, k \le n$ . Show that the entry in row $j$ , column $k$ of $A^3$ (which is defined to mean $AAA$ ) is

\sum_{p=1}^n \sum_{r=1}^n A_{j,p}A_{p,r}A_{r,k}

TODO