# How do you find the inverse of A=((6, -2), (9, -3))?

Feb 27, 2016

A has no inverse.

#### Explanation:

To find the inverse of a 2 X 2 matrix , consider the following.

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

ad - bc , is the determinant of the matrix , and if equal to zero , then no inverse exists and the matrix is singular.

for matrix here: a = 6 , b=-2 , c = 9 and d = -3

$a d - b c = \left(6 \times - 3\right) - \left(- 2 \times 9\right) = - 18 + 18 = 0$

result is that matrix A has no inverse.