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Identity Matrix

An identity matrix is a square matrix having 1s on the main diagonal, and 0s everywhere else.

For example, the 2 × 2 and 3 × 3 identity matrices are shown below.

[ 1 0 0 1 ]

[ 1 0 0 0 1 0 0 0 1 ]

These are called identity matrices because, when you multiply them with a compatible matrix , you get back the same matrix.

Example:

[ 1 0 0 1 ] ⋅ [ 4 7 − 1 3 ] = [ 1 ( 4 ) + 0 ( − 1 ) 1 ( 7 ) + 0 ( 3 ) 0 ( 4 ) + 1 ( − 1 ) 0 ( 7 ) + 1 ( 3 ) ]

= [ 4 7 − 1 3 ]