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.