The number of scalar additions required to compute $P(QR)$ Let $P$, $Q$, $R$ be matrices of order $3\times5, 5\times7$ and $7\times3$ respectively. What is the number of scalar additions required to compute $P(QR)$?
Do we have any formula to compute this? If we had to square a square matrix of order $n\times n$ how will the results change? Thanks...
Answer = $ 126 $. To get every number in the matrix $QR$, we need $6$ additions and there are $15$ numbers like that. similar calculation for the next step gives $4$ additions repeated $9$ times. So , we need $ 6*15 + 9*4 = 126 $ additions.
Just an observation is  that .. the dimension of the product Matrix P(QR) is $9(3 \times 3)$ and 9 is dividing 126 ...so from this way can we find the number of scalar addition of the matrix.