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Math Help - Matrix Multiplication question

  1. #1
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    Matrix Multiplication question

    Can a regular square matrix times any matrix of the same size equal zero?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Something like this?

    \left(\begin{array}{cc}1 & 2\\ 1&2\end{array} \right).\left(\begin{array}{cc}1 & 2\\ -\frac12&-1\end{array} \right) = \left(\begin{array}{cc}0 & 0\\ 0&0\end{array} \right)
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  3. #3
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    No, by regular matrix i mean inverse matrix
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  4. #4
    MHF Contributor Unknown008's Avatar
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    If you multiply a matrix by its inverse you get the identity matrix...

    \left(\begin{array}{cc}1 & 2\\ 3&4\end{array} \right).\left(\begin{array}{cc}-2 & 1\\ \frac32&-\frac12\end{array} \right) = \left(\begin{array}{cc}1 & 0\\ 0&1\end{array} \right)
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  5. #5
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    I know, but that again is not my question.

    Can you reach the zero matrix by multiplying an inverse square matrix with any other square matrix of the same size? (not the identity matrix, the zero matrix)
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  6. #6
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    Perhaps you mean invertible matrix. If A is an invertible matrix, then the only matrix, B, such that AB= 0 is the 0 matrix itself. To see that, multiply both sides of AB= 0 by A^{-1}.
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  7. #7
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    O, lol. Shame I don't study in English... It gets in the way sometimes
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