Prove that if $A$ and $B$ are both upper or lower triangular matrices, then the diagonal entries of both $AB$ and $BA$ are the products of the diagonal entries.
Attempt. Assuming the dimensions of matrices A and B allow their product to be successfully computed. I don't know how to go about this proof after this step.
Hint. I want the solution to this problem to be a simple as possible, while using techniques that are elementary by nature. So please, no definition of Matrix Multiplication or Summations. Thanks!