Associative Properties of Matrices:

The Associative Property of Addition for Matrices states:

Let A, B, and C be m × n matrices.  Then, (A + B) + C = A + (B + C).

Example:

Find (A + B) + C and A + (B + C)

        Find (A + B) + C:      

        

        Find A + (B + C):

        

The Associative Property of Multiplication of Matrices states:

Let A, B, and C be n × n matrices.  Then, (AB)C = A (BC). 

Example:

Find (AB)C and A (BC).

         Find (AB)C:                                                      Find A(BC):