NxN matrix multiplication; commutativity

[mathman44]

Homework Statement

Explicitly show, using numbers, that in general NxN matrix multiplication is not commutative. Show this for all N > 1.


If I make a matrix A, 2x2,

1 2
3 4

and multiply by matrix B, also 2x2

5 6
7 8

I get AB =/=BA

If I multiply a new matrix A, 3x3,

1 2 3
4 5 6
7 8 9

by a new matrix B, 3x3,

10 11 12
13 14 15
16 17 18

I get AB=/=BA

Ok... but how do I show that this holds for ALL n > 1? I have to do this explicitly using real numbers.

 

[ystael]

There is a simple way to make a smaller matrix into a larger matrix.

 

[tiny-tim]

hi mathman44!

Ok... but how do I show that this holds for ALL n > 1? I have to do this explicitly using real numbers.

try defining a matrix that's nearly all zeros, and a few 1s or -1s