$$\mathrm{S}=\left(\begin{array}{rr}-1 & 0 \0 & -1\end{array} ight), \alpha=\left(\begin{array}{ll}\mathrm{i} & 0 \0 & \mathrm{i}\end{array} ight) ext{ হলে, } \mathrm{S} \alpha^2 ext{ হলো- }$$

Question

$$\mathrm{S}=\left(\begin{array}{rr}-1 & 0 \0 & -1\end{array}ight), \alpha=\left(\begin{array}{ll}\mathrm{i} & 0 \0 & \mathrm{i}\end{array}ight) 	ext{ হলে, } \mathrm{S} \alpha^2 	ext{ হলো- }$$

Accepted Answer

$$\begin{aligned}\mathrm{S} \alpha_2=\left(\begin{array}{cc}-1 & 0 \0 & -1\end{aligned}ight)\left(\begin{array}{ll}\mathrm{i} & 0 \0 & \mathrm{i}\end{array}ight)\left(\begin{array}{ll}\mathrm{i} & 0 \0 & \mathrm{i}\end{array}ight) & \& =-\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight) 	imes \mathrm{i}\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight) 	imes \mathrm{i}\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight) \& =-\mathrm{i^2}\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight) 	imes\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight) 	imes\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight) \quad[\mathrm{I_{23}} =\mathrm{I_2}] \& =-\mathrm{i^2}\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight)=\left(\begin{array}{ll}1 & 0 \0 & 1\end{array}ight)=-\left(\begin{array}{cc}-1 & 0 \0 & -1\end{array}ight)=-\mathrm{S}\end{aligned}$$

Admission CU A প্রশ্নব্যাংক MCQ — \[\mathrm{S}=\left(\begin{array}{rr}-1 &amp; 0 \\0 &amp; -1\end{array}\r

আরো প্রশ্ন দেখো

Admission CU A প্রশ্নব্যাংক MCQ — \[\mathrm{S}=\left(\begin{array}{rr}-1 & 0 \\0 & -1\end{array}\r