A=[(1,i),(-i,1)] ,B=[(i,-1),(-1,-i)] এবং i=√-1 হলে AB = কত?

Explanation:

Another Explanation (5): bài toán: \(A=\begin{bmatrix} 1 & i \\ -i & 1 \end{bmatrix}\), \(B=\begin{bmatrix} i & -1 \\ -1 & -i \end{bmatrix}\), \(i=\sqrt{-1}\) হলে \(AB=?\) 🤔 সমাধান: \(AB = \begin{bmatrix} 1 & i \\ -i & 1 \end{bmatrix} \begin{bmatrix} i & -1 \\ -1 & -i \end{bmatrix}\) \( = \begin{bmatrix} (1 \times i + i \times -1) & (1 \times -1 + i \times -i) \\ (-i \times i + 1 \times -1) & (-i \times -1 + 1 \times -i) \end{bmatrix}\) \( = \begin{bmatrix} (i - i) & (-1 - i^2) \\ (-i^2 - 1) & (i - i) \end{bmatrix}\) যেহেতু \(i^2 = -1\), \( = \begin{bmatrix} 0 & (-1 - (-1)) \\ (-(-1) - 1) & 0 \end{bmatrix}\) \( = \begin{bmatrix} 0 & (-1 + 1) \\ (1 - 1) & 0 \end{bmatrix}\) \( = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}\) ✅ অতএব, \(AB = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}\). 🥳