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Question Number 104486 by Anindita last updated on 21/Jul/20

$$\mathbf{If}\mathbf{A}=\left[\begin{array}{ccc}3& -4& 2\\ -2& 1& 0\\ -1& -1& 1\end{array}\right]\mathbf{and}$$$$\mathbf{B}=\left[\begin{array}{ccc}1& 2& -2\\ 2& 5& -4\\ 3& 7& -5\end{array}\right]\mathbf{then}$$$$\mathbf{show}\mathbf{that}\mathbf{AB}=\mathbf{BA}={\mathbf{I}}_3.$$

Answered by OlafThorendsen last updated on 21/Jul/20

$$\mathrm{Just}\mathrm{calculate}{\mathrm{B}}^{-1}=\frac{1}{\mathrm{detB}}\mathrm{cov}{\left(\mathrm{B}\right)}^{\mathrm{T}}$$$$\mathrm{Then}{\mathrm{B}}^{-1}=\mathrm{A}$$$$\Rightarrow \mathrm{AB}={\mathrm{B}}^{-1}\mathrm{B}={\mathrm{I}}_3={\mathrm{BB}}^{-1}=\mathrm{BA}$$

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