Question
यदि $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&i\end{array}} \right]$ ओर $B = \left[ {\begin{array}{*{20}{c}}0&{ - i}\\{ - i}&0\end{array}} \right]$ तो $(A + B)(A - B)$
तथा $BA = \left[ {\begin{array}{*{20}{c}}0&{ - i}\\{ - i}&0\end{array}} \right]\left[ {\begin{array}{*{20}{c}}i&0\\0&i\end{array}} \right]\, = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]$
चूकि $AB = BA,$ अत: $(A + B)(A - B) = {A^2} - {B^2}$.
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$\overrightarrow {AB} \,\,.\,\,\overrightarrow {CD} \,\, + \,\overrightarrow {\,BC} \,\,.\,\,\overrightarrow {AD} \,\, + \overrightarrow {CA} \,\,.\,\,\overrightarrow {BD} \,\, = $