If A = bmatrix 2 & 1 \\ 3 & 4 bmatrix and B = bmatrix 1 & 0 \\ 2 & 1 bmatrix, what is the entry in row 1, column 1 of AB?

In a matrix product, the entry in row 1, column 1 of $AB$ is the dot product of row 1 of $A$ with column 1 of $B$. Row 1 of $A$ is $(2, 1)$ and column 1 of $B$ is $(1, 2)$, so the entry is $(2)(1)+(1)(2)=2+2=4$, choice D. Choice A uses only the first product, $2\cdot 1$, and forgets to add the second. Choice B is the (1,1) entry of $A+B$, which comes from adding matrices instead of multiplying them. Choice C pairs the wrong entries, such as combining the numbers in the first column of $A$ ($2$ and $3$), instead of matching a row of $A$ to a column of $B$.