A) \[{{A}^{2}}-{{B}^{2}}\]
B) \[{{A}^{2}}+{{B}^{2}}\]
C) \[{{A}^{2}}-{{B}^{2}}+BA+AB\]
D) None of these
Correct Answer: A
Solution :
Here \[AB=\left[ \begin{matrix} i & 0 \\ 0 & i \\ \end{matrix} \right]\,\left[ \begin{matrix} 0 & -i \\ -i & 0 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] and \[BA=\left[ \begin{matrix} 0 & -i \\ -i & 0 \\ \end{matrix} \right]\left[ \begin{matrix} i & 0 \\ 0 & i \\ \end{matrix} \right]\,=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] Since \[AB=BA,\]therefore\[(A+B)(A-B)={{A}^{2}}-{{B}^{2}}\].You need to login to perform this action.
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