# Show that Matrix Multiplication is Associative

## Homework Statement

Show that (AB)C=A(BC)

I am just trying to do this to try to gain some experience with problems like this. I saw in my text that they did a similar example for distributivity using the definition of matrix multiplication, so I thought I could use that approach.

## The Attempt at a Solution

Let the (i,j)-entry of A be given by aij
Let the (i,j)-entry of B be given by bij
Let the (i,j)-entry of C be given by cij

Then the (i,j)-entry of (AB) is given by

$$\sum_{k=1}^na_{ik}b_{kj}$$

Here is where I get lost. I was thinking of then writing that the (i,j)-entry of (AB)C would be given by

$$\sum_{k=1}^n(a_{ik}b_{kj})c_{kj}$$

but I don't think that this works.....and I am not sure why or why not

Any hints?

Thanks!

Related Calculus and Beyond Homework Help News on Phys.org
Office_Shredder
Staff Emeritus