Explore BrainMass
Share

Explore BrainMass

    Proving some identities of invertble matrices

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Can you help me prove the following:

    If A is an invertible matrix and n is a non negative integer then:

    a) A^-1 is invertible and (A^-1)^-1 = A

    b) A^n is invertible and (A^n)^-1 = A^-n = (A^-1)^n

    Please show all work in detail

    © BrainMass Inc. brainmass.com October 10, 2019, 4:52 am ad1c9bdddf
    https://brainmass.com/math/matrices/proving-some-identities-invertble-matrices-481304

    Solution Preview

    The proofs are on the file: Algebra.doc

    Prove the following:

    If A is an invertible matrix and n is a non negative integer then:

    a) A^-1 is invertible and (A^-1)^-1 = A
    Proof. As A is invertible, if we denote its inverse by , then
    ...

    Solution Summary

    This solution consists of detailed proofs of the following statements:

    If A is an invertible matrix and n is a non negative integer, then

    a) A^-1 is invertible and (A^-1)^-1 = A

    b) A^n is invertible and (A^n)^-1 = A^-n = (A^-1)^n

    $2.19