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|.

Answer 1

\[A = \begin{bmatrix} 0 & i\\i & 1 \end{bmatrix} \] 
\[ \Rightarrow \left| A \right| = 0 - i^2 \] 
\[ = - \left( - 1 \right) = 1\] 
Also,

\[B = \begin{bmatrix} 0 & 1\\1 & 0 \end{bmatrix} \] 
\[ \Rightarrow \left| B \right| = 0 - 1 = - 1 \] 
So,
\[\left| A \right| + \left| B \right| = 1 - 1 = 0\]