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Question
If \[A = \begin{bmatrix}0 & i \\ i & 1\end{bmatrix}\text{ and }B = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\] , find the value of |A| + |B|.
Solution
\[A = \begin{bmatrix} 0 & i\\i & 1 \end{bmatrix} \]
\[ \Rightarrow \left| A \right| = 0 - i^2 \]
\[ = - \left( - 1 \right) = 1\]
Also,
\[B = \begin{bmatrix} 0 & 1\\1 & 0 \end{bmatrix} \]
\[ \Rightarrow \left| B \right| = 0 - 1 = - 1 \]
So,
\[\left| A \right| + \left| B \right| = 1 - 1 = 0\]
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