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**Prove It** No, an identity matrix is not equal to 1. It ACTS LIKE a 1 when you are dealing with matrices.

And you can't ALWAYS use $\displaystyle I_2$ because the matrices you are working with might not be $\displaystyle 2 \times 2$. It depends on the dimensions of the matrices you are working with. In this case you use $\displaystyle I_2$ because the matrices you are working with are $\displaystyle 2 \times 2$.

But what if you were dealing with $\displaystyle 3 \times 3$ matrices?

Which $\displaystyle I$ would you use then?