Algebra and Trigonometry 10th Edition

The general form of a matrix of order $2 \times 2$ is: $det \ A=\begin{bmatrix} p & q \\ r & s\end{bmatrix}=ps-qr$ We can determine the inverse of the matrix $A$ as follows: $A^{-1}=\dfrac{1}{det \ A} \begin{bmatrix} s & -q \\ -r & p\end{bmatrix}$ Now, $det \ A =\begin{bmatrix} -12 & 6 \\ 10 & -5 \end{bmatrix}=60-60= 0$ This means that no inverse is possible.