Two matrices $A$ and $B$ can be multiplied to give $AB$ if and only if:
ABoth are square matrices
BThey have the same order
CThe number of columns of $A$ equals the number of rows of $B$
DBoth have the same number of rows
Answer & Solution
Correct answer: C. The number of columns of $A$ equals the number of rows of $B$
For matrix multiplication $A \cdot B$, the inner dimensions must match. If $A$ is $m \times n$ and $B$ is $p \times q$, then $AB$ exists only when $n = p$, and the result has order $m \times q$.
Note: $AB$ existing does not mean $BA$ exists. Even when both exist, they are usually different matrices ($AB \neq BA$ in general). Matrix multiplication is not commutative.
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