Chapter 6, Matrices and Determinants - Section 6.3 - Inverses of Matrices and Matrix Equations - 6.3 Exercises - Page 523: 16

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We find the determinant $(ad-bc)$ $2-5/3=1/3$ Use the formula \[ M=\frac{1}{ad-bc} \left[ {\begin{array}{cc} d &-b \\ -c & a \\ \end{array} } \right] \] to get \[ M= 3 \left[ {\begin{array}{cc} 4 & -1/3 \\ -5 & 1/2 \\ \end{array} } \right] \] or \[ M= \left[ {\begin{array}{cc} 12 & -1 \\ -15 & 3/2 \\ \end{array} } \right] \]