# Multiplying upper triangular matrices

Suppose that $A$ and $B$ are $n$ dimensional, upper triangular matrices. How many floating point multiplications are necessary to compute $AB$?

Typically a $$nxn$$ matrix requires $$n^2$$ multiplications with a vector. Thus multiplying 2 $$nxn$$ matrices would require $$2n^2$$ multiplications and $$2n (n-1)$$ operations to sum the products.