In^-1=In Lin alg

1. Mar 29, 2009

cleopatra

1. The problem statement, all variables and given/known data

In^-1=In
proof that!

2. Relevant equations
1 0
0 1
= I2^-1= I2 for an example.

2. Mar 29, 2009

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 $$I_n$$?

3. Mar 29, 2009

cleopatra

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

4. Mar 29, 2009

cleopatra

anyone?

5. Mar 29, 2009

yyat

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 $$I_nI_n=I_n$$.