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Math Help - Complex Numbers- Matrices

  1. #1
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    Complex Numbers- Matrices

    Consider J is an element of M2(R) given by: [0 -1
    1 0]
    Consider the set C as a subset of M2(R) defined as : C= {aI + bJ| a,b are elements of R}
    Show that the products and sums of C are again in C. Which elements of C are invertible?
    Is C together with addition and multiplication of matrices a field?
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  2. #2
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    Quote Originally Posted by amm345 View Post
    Consider J is an element of M2(R) given by: [0 -1
    1 0]
    Consider the set C as a subset of M2(R) defined as : C= {aI + bJ| a,b are elements of R}
    Show that the products and sums of C are again in C. Which elements of C are invertible?
    Is C together with addition and multiplication of matrices a field?
    What determines whether a matrix is invertible?

    Suppose that det(C) = 0. What does this tell you about a and b in relation to which elements are invertible? (just calculate det(C) and set equal to zero) This should be intuitive.
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