Seja \( A=\left|\begin{array}{ll}1 & 1 \\ 3 & 1\end{array}\right| \quad B=\left|\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right| \quad \) Carculi: a) \( A^{-1} \)

Find the inverse matrix of \( \begin{pmatrix} 1 & 1 \\ 3 & 1 \end{pmatrix} \). Matrices by following steps: - step0: Find the matrix inverse: \(\left[\begin{array}{rr}{1}&{1}\\{3}&{1}\end{array}\right]\) - step1: Evaluate the determinant: \(-2\) - step2: Using the formula: \(\frac{1}{1\times 1-1\times 3}\times \left[\begin{array}{rr}{1}&{-1}\\{-3}&{1}\end{array}\right]\) - step3: Evaluate: \(-\frac{1}{2}\times \left[\begin{array}{rr}{1}&{-1}\\{-3}&{1}\end{array}\right]\) - step4: Multiply the terms: \(\left[\begin{array}{rr}{-\frac{1}{2}\times 1}&{-\frac{1}{2}\left(-1\right)}\\{-\frac{1}{2}\left(-3\right)}&{-\frac{1}{2}\times 1}\end{array}\right]\) - step5: Evaluate: \(\left[\begin{array}{rr}{-\frac{1}{2}}&{\frac{1}{2}}\\{\frac{3}{2}}&{-\frac{1}{2}}\end{array}\right]\) A matriz inversa de \( A \) é dada por: \[ A^{-1} = \begin{bmatrix} -\frac{1}{2} & \frac{1}{2} \\ \frac{3}{2} & -\frac{1}{2} \end{bmatrix} \]