The <diagonal matrix entry> is $D_{ii}=\sum_{k=1}^N B_{ik}C_{ki}$. Only $k=i$ can contribute, so \b[$D_{ii}=B_{ii}C_{ii}$]. This also shows that the product is a <diagonal matrix>, with its diagonal obtained by entrywise multiplication of the two diagonals.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 4 / a / ii / Solution

 Solution (source code)