Q.A company sells two products, P and Q, at two branches, Branch I and Branch II. The sales matrix for one month is $A=\begin{pmatrix}120&80\\95&110\end{pmatrix}$ and for the following month is $B=\begin{pmatrix}130&90\\100&105\end{pmatrix}$, where rows represent Branch I and Branch II respectively, and columns represent product P and product Q respectively. Find the total two-month sales matrix, and state the total sales of product P at Branch I over the two months.

Total sales over two months is found by simply adding the two months' sales matrices element-by-element, since each position of the matrix represents the same branch-product combination in both months.

Adding the two months' sales matrices

Since both matrices use the SAME row/column meaning (row 1 = Branch I, row 2 = Branch II, column 1 = P, column 2 = Q), the total over both months is simply $A+B$, added element-by-element:

Reading off Branch I's total sales of product P

Branch I is row 1, product P is column 1, so the required figure is the $(1,1)$ entry of $A+B$, which is $250$ units. …

Adding entries from different rows/columns across the two matrices (e.g. adding Branch I's P-sales in month 1 to Branch II's Q-sales in month 2) instead of matching each branch-product position exactly — matrix additio …