As the question asked for minimum algebraic operations, so when a number is to be multiplied with zero, it will not be counted.
Consider the following example:
$P = \begin{bmatrix} 1 & 0 & 0 & 0& 0 \\ 2 & 2 & 0& 0 & 0 \\ 3 & 3 & 3 & 0 & 0 \\ 4 & 4 & 4 & 4 & 0 \\ 5 & 5 & 5 & 5 & 5 \end{bmatrix}$
$Q = \begin{bmatrix} 5 & 5 & 5 & 5 & 5 \\ 0 & 4 & 4 & 4 & 4 \\ 0 & 0 & 3& 3 & 3 \\ 0 & 0 & 0 & 2 & 2 \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix}$
For first row and first column only multiplication of $1$ with $5$ will be considered, rest will be ignored.
For second row and second column, only multiplication of $2 \times 5$ and $2 \times 4$ will be considered, rest will be ignored.
So, $\begin{bmatrix} 1,0 & 1,0 & 1,0 & 1,0 & 1,0 \\ 1,0 & 2,1 &2,1 &2,1 &2,1 \\ 1, 0 & 2, 1 & 3,2 & 3,2, & 3,2 \\ 1,0 & 2,1 & 3,2 & 4,3 & 4,3 \\ 1,0 & 2,1 & 3,2 & 4,3 & 5,4 \end{bmatrix}$
$x \rightarrow $ number of multiplications
$y \rightarrow$ number of addition
The sum comes out to be $85.$