A^2=E 행렬 곱

[출제의도] 행렬의 연산법칙으로 문제해결하기 $\displaystyle A \begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 5 \\ 4 \end{pmatrix}$의 양변에 행렬A를 곱하면 $\displaystyle {A} ^{2} \begin{pmatrix} 4 \\ 3 \end{pmatrix} = A \begin{pmatrix} 5 \\ 4 \end{pmatrix} = \begin{pmatrix} 4 \\ 3 \end{pmatrix}$, $\displaystyle A \begin{pmatrix} 4 & 5 \\ 3 & 4 \end{pmatrix} = \begin{pmatrix} 5 & 4 \\ 4 & 3 \end{pmatrix}$ $\displaystyle A = \begin{pmatrix} 5 & 4 \\ 4 & 3 \end{pmatrix} {\begin{pmatrix} 4 & 5 \\ 3 & 4 \end{pmatrix}} ^{-1} = \begin{pmatrix} 8 & - 9 \\ 7 & - 8 \end{pmatrix}$ $\displaystyle A \begin{pmatrix} 3 \\ - 1 \end{pmatrix} = {\begin{pmatrix} 8 & - 9 \\ 7 & - 8 \end{pmatrix}} \begin{pmatrix} 3 \\ - 1 \end{pmatrix} = \begin{pmatrix} 33 \\ 29 \end{pmatrix}$ $\therefore 33 + 29 = 62$