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Why is he called the identity?

Remember the multiplicative identity for regular numbers?

What can you multiply 3 by so he stays a 3?

1!

3 times 1 = 3

AND

1 times 3 = 3

It works both ways!

It's the same for our identity matrix!

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

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

 
A times I = A

AND

I times A = A

By the way, this guy is the 2 x 2 identity:

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

So, what's the 3 x 3 identity?

I = [ row 1: 1 , 0 , 0  row 2: 0 , 1 , 0  row 3: 0 , 0 , 1 ]

The 4 x 4 identity?

I = [ row 1: 1 , 0 , 0 , 0  row 2: 0 , 1 , 0 , 0  row 3: 0 , 0 , 1 , 0  row 4: 0 , 0 , 0 , 1 ] ... Get the pattern? ... It's ones down the main diagonal and zeros everywhere else.

*All identity matrices are square.