Manakah yang saling invers: a. \( \left(\begin{array}{ll}3 & 5 \\ 2 & 3\end{array}\right) \) dan \( \left(\begin{array}{cc}-3 & 5 \\ 2 & -3\end{array}\right) \quad \) c. \( \left(\begin{array}{cc}4 & 3 \\ 1 & 1\end{array}\right) \) dan \( \left(\begin{array}{cc}1 & -3 \\ -1 & 4\end{array}\right) \) b. \( \left(\begin{array}{cc}-3 & 7 \\ -4 & 9\end{array}\right) \) dan \( \left(\begin{array}{ll}9 & -7 \\ 4 & -3\end{array}\right) \quad \) d. \( \left(\begin{array}{cc}6 & -5 \\ -5 & 4\end{array}\right) \) dan \( \left(\begin{array}{cc}-4 & -5 \\ -5 & -6\end{array}\right) \) A. a saia B. a dan b saia C. a, b.danc D. semyanya

A. a. \( \left(\begin{array}{ll}3 & 5 \\ 2 & 3\end{array}\right) \) dan \( \left(\begin{array}{cc}-3 & 5 \\ 2 & -3\end{array}\right) \) adalah invers salingnya Untuk mengecek apakah dua matriks saling invers, kita harus memeriksa apakah perkalian matriks tersebut menghasilkan matriks identitas. Matriks identitas adalah matriks yang setiap elemennya di diagonal adalah 1 dan elemennya di luar diagonal adalah 0. 1. Untuk matriks \( \left(\begin{array}{ll}3 & 5 \\ 2 & 3\end{array}\right) \) dan \( \left(\begin{array}{cc}-3 & 5 \\ 2 & -3\end{array}\right) \): \[ \left(\begin{array}{ll}3 & 5 \\ 2 & 3\end{array}\right) \times \left(\begin{array}{cc}-3 & 5 \\ 2 & -3\end{array}\right) = \left(\begin{array}{cc}3 \times (-3) + 5 \times 2 & 3 \times 5 + 5 \times (-3) \\ 2 \times (-3) + 3 \times 2 & 2 \times 5 + 3 \times (-3)\end{array}\right) = \left(\begin{array}{cc}-9 + 10 & 15 - 15 \\ -6 + 6 & 10 - 9\end{array}\right) = \left(\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right) \] 2. Untuk matriks \( \left(\begin{array}{cc}-3 & 7 \\ -4 & 9\end{array}\right) \) dan \( \left(\begin{array}{ll}9 & -7 \\ 4 & -3\end{array}\right) \): \[ \left(\begin{array}{cc}-3 & 7 \\ -4 & 9\end{array}\right) \times \left(\begin{array}{ll}9 & -7 \\ 4 & -3\end{array}\right) = \left(\begin{array}{cc}-3 \times 9 + 7 \times 4 & -3 \times (-7) + 7 \times (-3) \\ -4 \times 9 + 9 \times 4 & -4 \times (-7) + 9 \times (-3)\end{array}\right) = \left(\begin{array}{cc}-27 + 28 & 21 - 21 \\ -36 + 36 & 28 - 27\end{array}\right) = \left(\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right) \] 3. Untuk matriks \( \left(\begin{array}{cc}6 & -5 \\ -5 & 4\end{array}\right) \) dan \( \left(\begin{array}{cc}-4 & -5 \\ -5 & -6\end{array}\right) \): \[ \left(\begin{array}{cc}6 & -5 \\ -5 & 4\end{array}\right) \times \left(\begin{array}{cc}-4 & -5 \\ -5 & -6\end{array}\right) = \left(\begin{array}{cc}6 \times (-4) + (-5) \times (-5) & 6 \times (-5) + (-5) \times (-6) \\ (-5) \times (-4) + 4 \times (-5) & (-5) \times (-5) + 4 \times (-6)\end{array}\right) = \left(\begin{array}{cc}-24 + 25 & -30 + 30 \\ 20 - 20 & 25 - 24\end{array}\right) = \left(\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right) \] 4. Untuk matriks \( \left(\begin{array}{cc}4 & 3 \\ 1 & 1\end{array}\right) \) dan \( \left(\begin{array}{cc}1 & -3 \\ -1 & 4\end{array}\right) \): \[ \left(\begin{array}{cc}4 & 3 \\ 1 & 1\end