A good answer might be:


10   0  20
20  40  10
 0  20  10

-2   2 
 1   1
 2  -2
= 10

1   0   2
2   4   1
0   2   1

-2   2 
 1   1
 2  -2
= 10

2  -2
2   6
4   0
= 20

1  -1
1   3
2   0

Associative

Multiply the first two following matrices together. Click on the = to check your result. Then multiply the result with the third matrix.

Problem Partial Result Result

  
 1  -1
 2   3
  

  
 -2  1
  0  2
  

  
 -1  0
  1  1
  

    
-1  0
 1  1
    

Now do the problem again, but this time start by multiplying the last two matrices.

Problem Partial Result Result

  
 1  -1
 2   3
  

  
 -2  1
  0  2
  

  
 -1  0
  1  1
  

 1 -1
 2  3

The final answer is the same for both ways of doing the problem. This demonstates the fact that matrix multiplication is associative:

(AB)C = A(BC)

Of course, the inner dimension of A and B must be the same, and the inner dimension of B and C must be the same. Usually a product of three matrices is written ABC.

QUESTION 11:

Say that A5×5 B C3×4 = D.

What are the dimensions of B and D?