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Math Help - matrix power

  1. #1
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    matrix power

    Is there mathematical proof for A^2*A=A*A^2 (A stands for square matrix)?
    Thanks in advance
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  2. #2
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    Re: matrix power

    Quote Originally Posted by jojo7777777 View Post
    Is there mathematical proof for A^2*A=A*A^2 (A stands for square matrix)?
    Thanks in advance
    \displaystyle \begin{align*} A^2 &= A \cdot A \\ A^2 \cdot A &= A \cdot A \cdot A \end{align*}

    and

    \displaystyle \begin{align*} A^2 &= A \cdot A \\ A \cdot A^2 &= A \cdot A \cdot A \end{align*}

    Therefore \displaystyle \begin{align*} A^2 \cdot A = A \cdot A^2 \end{align*}.
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    Re: matrix power

    Thank you!!!
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