# In^-1=In Lin alg

#### cleopatra

1. Homework Statement

In^-1=In
proof that!

2. Homework Equations
1 0
0 1
= I2^-1= I2 for an example.

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#### yyat

The inverse matrix $$A^{-1}$$ of $$A$$ is by definition the matrix such that $$A^{-1}A=I_n$$ and $$AA^{-1}=I_n$$. So is $$I_n$$ the inverse of $$I_n$$?

#### cleopatra

yes In is the inverese of In because In^-1 is the inverse of In and In^-1=In
true?

anyone?

#### yyat

yes In is the inverese of In because In^-1 is the inverse of In and In^-1=In
true?
Just use the definition. You want to check that the inverse of $$I_n$$ is $$I_n$$ itself (this is just another way of saying $$I_n^{-1}=I_n$$). What it comes down to is that $$I_nI_n=I_n$$.

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