howmany algebraic operations are needed in matrix multiplication

Question

I am not exactly getting the question, could anyone help me by an example?

(1) How many algebraic operations $(+,-,\times , /)$ are nessesary to multiply a $n\times n$ real matrix by a real $n$ touple vector?

(2) same question as above but to solve $Ax=b$ where $A$ is an upper triangular matrix having no element as $0$

Answer 1

Suppose $AB = Q$

Each element in $Q$ is created when a row of $A$ multiplies by a column of $B.$

or $q_{i,j} = \sum_\limits{k = 1}^n a_{i,k}b_{k,j}$

For each element in $Q$ then there are $n$ multiplication operations and $(n-1)$ addition operations.

And there are $n^2$ elements in $Q.$

Can you apply similar logic for your second question?