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Math Help - Matrix True And False Statements

  1. #1
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    Matrix True And False Statements

    Hi I just wanted to double check the answers for these T/F Matrix statements, hopefully they are simple to determine for you guys...

    Which of the following statements are true for all A and B invertible nn matrices?

    1. AB=I does not imply that BA=I.

    2. The columns of B span Rn.

    3. B can have two identical rows.

    4. The homogeneous system Bv=0 has only the trivial solution.

    5. The matrix AT is invertible.

    6. (ABA^1)^3=AB^3A^1

    7. A^7B^5 is invertible

    8. (AB)^1=A^1B^1

    9. A+A^1 is invertible

    10. (A+B)(AB)=A^2B^2

    Thank you!
    Last edited by UBCBOY; February 24th 2013 at 06:26 PM.
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  2. #2
    Senior Member vincisonfire's Avatar
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    Re: Matrix True And False Statements

    What is your sequence of answers?
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  3. #3
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    Re: Matrix True And False Statements

    1. T
    2. F
    3. T
    4. F
    5. T
    6. F
    7.t
    8. T
    9. F
    10. F
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  4. #4
    Senior Member vincisonfire's Avatar
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    Re: Matrix True And False Statements

    Some of the statements are unclear to me.
    Let me start with 1.
    AB=I does not imply that BA=I. Since A is invertible inv(A)AB = inv(A)I or B = inv(A). Which means that A inv(A)=I does not imply that inv(A) A=I. The first statement is thus false.
    I think you should reconsider your answers. The binomial inverse theorem may help. Binomial inverse theorem - Wikipedia, the free encyclopedia
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