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Properties of Inverse Matrices

  • Thread starter tigger1989
  • Start date
  • #1

Homework Statement



Determine which of the formulas hold for all invertible nxn matrices A and B

A. AB=BA
B. (A+A^–1)^8=A^8+A^–8
C. A^5 is invertible
D. A+A^–1 is invertible
E. (In+A)(In+A^–1)=2In+A+A^–1 (where In is the identity matrix)
F. (A+B)^2=A^2+B^2+2AB

Homework Equations



Certain properties of inverse matrices can be used. For example, if A is invertible, then A^k is invertible for all k greater or equal to 1 (this proves C to be correct).

The Attempt at a Solution



I was able to find counterexamples to prove A and B and F incorrect. However, the webwork program (designed for practicing basic Linear Algebra) I am using states that C, D, and E are not all correct ... what am I missing?
 

Answers and Replies

  • #2
172
2
Option D is not always true. Try to find a matrix A where [tex]A^{-1} = -A[/tex].
 

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