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In^-1=In Lin alg

  • Thread starter cleopatra
  • Start date
1. Homework Statement

In^-1=In
proof that!

2. Homework Equations
1 0
0 1
= I2^-1= I2 for an example.
 
316
0
The inverse matrix [tex]A^{-1}[/tex] of [tex]A[/tex] is by definition the matrix such that [tex]A^{-1}A=I_n[/tex] and [tex]AA^{-1}=I_n[/tex]. So is [tex]I_n[/tex] the inverse of [tex]I_n[/tex]?
 
yes In is the inverese of In because In^-1 is the inverse of In and In^-1=In
true?
 
anyone?
 
316
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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 [tex]I_n[/tex] is [tex]I_n[/tex] itself (this is just another way of saying [tex]I_n^{-1}=I_n[/tex]). What it comes down to is that [tex]I_nI_n=I_n[/tex].
 

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