- #1

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## 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 a

_{ij}

Let the (i,j)-entry of

**B**be given by b

_{ij}

Let the (i,j)-entry of

**C**be given by c

_{ij}

Then the (i,j)-entry of (

**AB**) is given by

[tex]\sum_{k=1}^na_{ik}b_{kj}[/tex]

Here is where I get lost. I was thinking of then writing that the (i,j)-entry of (

**AB**)

**C**would be given by

[tex]\sum_{k=1}^n(a_{ik}b_{kj})c_{kj}[/tex]

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

Any hints?

Thanks!