For $A\in\mathbb F^{m\times n}$ and $B\in\mathbb F^{n\times p}$, the product $AB\in\mathbb F^{m\times p}$ has entries $(AB)_{ij}=\sum_{k=1}^n a_{ik}b_{kj}$. Multiply a row of $A$ by a column of $B$ and sum. The inner dimensions must match; the outer dimensions give the result's shape.
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