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Math Help - Find an expression for B inverse in terms of B

  1. #1
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    Find an expression for B inverse in terms of B

    Hi everyone,

    I am stuck on this question, because I do not know any properties for square matrices when you multiply them together. I'm not sure what the question is asking, so any insight would be helpful

    Suppose that B is an m by m matrix that satisfies the following equation:

    B^5 + B^3 + B^2 = I (identity matrix)

    Find an expression for B inverse in terms of B.


    Is there a rule for square matrices when you multiply them by themselves?
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  2. #2
    Master Of Puppets
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    If you keep mulitplying both sides by \displaystyle  B^{-1}

    you should be able to isolate \displaystyle  B in terms of \displaystyle  B^{-1}
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by KelvinScc View Post
    Hi everyone,

    I am stuck on this question, because I do not know any properties for square matrices when you multiply them together. I'm not sure what the question is asking, so any insight would be helpful

    Suppose that B is an m by m matrix that satisfies the following equation:

    B^5 + B^3 + B^2 = I (identity matrix)

    Find an expression for B inverse in terms of B.


    Is there a rule for square matrices when you multiply them by themselves?
    Since B is invertable just multiply the equation by its inverse

    B^{-1}(B^5 + B^3 + B^2) = B^{-1}I

    Since matrix multiplication distributes and we know that

    B^{-1}B=I we are done!
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  4. #4
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    Or, same idea "in reverse", factor out a B:
    B^5 + B^3 + B^2=  B(B^4+ B^2+ B)= (B^4+ B^2+ B)B= I and it should be obvious what the inverse of B is, as long as you just know the definition of "inverse".
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