Proof that In^-1=In | Linear Algebra

[cleopatra]

Homework Statement

In^-1=In
proof that!

Homework Equations

1 0
0 1
= I2^-1= I2 for an example.

 

[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?

 

[cleopatra]

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 $$I_nI_n=I_n$$.