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The Identity Matrix

Remember how I said that matrix multiplication is NOT commutative? Most of the time?
 

Try these multiplications:

A = [ row 1: 2 , -6 row 2: -5 , 8 ] B = [ row 1: 1 , 0 row 2: 0 , 1 ]


A times B
 

B times A


Whoa, Dude!

You should have noticed two funky things:

1 You got the same thing for both
 

A times B = B times A
2 You got A for both answers!
        There was just no getting rid of that guy!


There's a good explanation for both of these things:

That B matrix I gave you is a very special guy -- So special that he gets his own letter and name:
 

THE IDENTITY MATRIX:

I = [ row 1: 1 , 0 row 2: 0 , 1 ]