Question

How many ways are there to order the evaluation of the product of n matrices: M 1 M 2 . . . M n ? For example, with two matrices, we have (M 1 M 2 )M 3 and M 1 (M 2 M3).

Answer 1

n-1 ways

Explanation:

since there are 2 ways to order 3 matrices:

`(M_1M_2)M_3` and
`M_1(M_2M_3)`

you can do it the same way for 4 matrices and notice a pattern:

`(M_1M_2)M_3M_4\\M_1(M_2M_3)M_4\\M_1M_2(M_3M_4)\\`

the pattern here is that the number of ways to order the evaluation of multiplying matrices is 1 less than the number of matrices.

for
`n` matrices the order is
`n-1`

hope this helps!