Hey all,

I've got a question that I'm having a little trouble with. I understand what the identity matrix is and how it works, but am unsure how to clearly show this. The question is as follows.

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Let I be a n x n matrix whose entry in row i and column j is

{ 1 if i = j

{ 0 if i != j

*This is an identity matrix

Show that AI = IA = A for every n x n matrix A.

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Once again I know that this statement is true as I know what the identity matrix is and when I use the identity matrix I understand why this works, but I am unsure how I would clearly show this. Any help is greatly appreciated. Thank you very much!