# Linear Algebra Proof using induction

• March 13th 2013, 08:33 PM
widenerl194
Linear Algebra Proof using induction
I'm having trouble starting because I haven't done induction in a long time. The problem says:

Let A be an n x n invertible matrix. Prove that for all m in the naturals, Am is invertible and determine a formula for its inverse in terms of A-1. Hint: use induction. My professor told us to only do this for m=2 and m=3.

Any help would be greatly appreciated!
• March 13th 2013, 11:24 PM
Gusbob
Re: Linear Algebra Proof using induction
For the induction step use
$(A^{k})(A^k)^{-1}=I \Leftrightarrow A(A^k)(A^k)^{-1}=A \Leftrightarrow (A^{k+1})(A^k)^{-1}A^{-1}=AA^{-1}=I$

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