포털:고등학교/수학/수학 I/문항

$Q1\mathrm{.}$ 행렬 $A\mathrm{=}\left(\begin{array}{cc}3& 2\\ 1& 1\end{array}\right)$에 대하여 $A\mathrm{+}{A}^{\mathrm{-}1}$의 모든 성분의 합을 구하라.

$A\mathrm{=}\left(\begin{array}{cc}a& b\\ c& d\end{array}\right),A^{\mathrm{-}1}\mathrm{=}\frac{1}{ad\mathrm{-}bc}\left(\begin{array}{cc}d& \mathrm{-}b\\ \mathrm{-}c& a\end{array}\right)$

$A^{\mathrm{-}1}\mathrm{=}\left(\begin{array}{cc}1& -2\\ -1& 3\end{array}\right)$

$\begin{array}{ccc}A\mathrm{+}{A}^{\mathrm{-}1}& \mathrm{=}& \left(\begin{array}{cc}3& 2\\ 1& 1\end{array}\right)\mathrm{+}\left(\begin{array}{cc}1& -2\\ -1& 3\end{array}\right)\\ & \mathrm{=}& \left(\begin{array}{cc}4& 0\\ 0& 4\end{array}\right)\end{array}$

$\begin{array}{cc}& 4\mathrm{+}0\mathrm{+}4\mathrm{+}0\mathrm{=}8\\ & \mathrm{\therefore }8\end{array}$