Suppose That $\boldsymbol { A } , \boldsymbol { B }$

Suppose that $\boldsymbol { A } , \boldsymbol { B }$ , and $\boldsymbol { C }$ are $3 \times 4,4 \times 5$ , and $5 \times 6$ matrices of numbers, respectively. Is it more efficient to compute the product $\boldsymbol { A B C }$ as $( \boldsymbol { A B } ) \boldsymbol { C }$ or as $\boldsymbol { A } ( \boldsymbol { B } \boldsymbol { C } )$ ? Justify your answer by computing the number of multiplications of numbers needed each way.