# How do you find the inverse of A=((6, 3), (4, 6))?

Feb 15, 2016

$\left(\begin{matrix}\frac{1}{4} & - \frac{1}{8} \\ - \frac{1}{6} & \frac{1}{4}\end{matrix}\right)$

#### Explanation:

For any matrix

$A = \left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$

then the inverse matrix is found as follows:

${A}^{-} 1 = \frac{1}{a d - b c} \left(\begin{matrix}d & - b \\ - c & a\end{matrix}\right)$

ad - bc , is called the 'determinant ,and it's value determines whether an inverse matrix exists or not.

If tdet(A) = 0 ,then inverse does not exist and matrix is said to be singular.

using the values from the question :

ad - bc = $\left(6 \times 6\right) - \left(3 \times 4\right) = \text{24 , hence matrix exists}$

$\frac{1}{24} \left(\begin{matrix}6 & - 3 \\ - 4 & 6\end{matrix}\right) = \left(\begin{matrix}\frac{1}{4} & - \frac{1}{8} \\ - \frac{1}{6} & \frac{1}{4}\end{matrix}\right)$