Math Is Fun Forum

EPhillips1989

Member

Registered: 2007-11-03

Posts: 29

matrices

hey can anyone give an example of a 3*3 matrix A and B such that AB does not equal BA

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: matrices

In general, matrices do not have a commutative property of multiplication. That means that usually AB≠BA.

A simple set of 3x3 matrices that springs to mind are these:

[ 1 1 1 ]
[ 0 0 0 ] = A
[ 0 0 0 ]

[ 1 0 0 ]
[ 1 0 0 ] = B
[ 1 0 0 ]

Multiplying AB wield yield:
[ 3 0 0 ]
[ 0 0 0 ]
[ 0 0 0 ]

But multiplying BA will give you:
[ 1 1 1 ]
[ 1 1 1 ]
[ 1 1 1 ]

Hope that helps.

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: matrices

for what its worth, when two matrices are such that AB = BA, the matrices A and B are said to "commute". But the fact is, most unequal matrices do not commute. So you probably could have picked any random matrix and it would have worked. Note, NullRoot choose matrices with lots of zeros to make it easier to multiply.

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A logarithm is just a misspelled algorithm.