# How do you find the inverse of A=((3, 0), (4, 17))?

Nov 10, 2016

The inverse is ${A}^{- 1} = \left(\begin{matrix}\frac{1}{3} & 0 \\ - \frac{4}{51} & \frac{1}{17}\end{matrix}\right)$

#### Explanation:

The inverse of a matrix $\left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$ is $= \frac{1}{a d - b c} \left(\begin{matrix}d & - b \\ - c & a\end{matrix}\right)$

Here $A = \left(\begin{matrix}3 & 0 \\ 4 & 17\end{matrix}\right)$

The determinant of the matrix is $= \left(3 \cdot 17 - 4 \cdot 0\right) = 51$

The determinant $\ne 0$, therefore it is invertible.

So, ${A}^{- 1} = \frac{1}{51} \left(\begin{matrix}17 & 0 \\ - 4 & 3\end{matrix}\right) = \left(\begin{matrix}\frac{1}{3} & 0 \\ - \frac{4}{51} & \frac{1}{17}\end{matrix}\right)$

Verification
A*A^(-1)=((3,0),(4,17))*((1/3,0),(-4/51,1/17)))=((1,0),(0,1))=I
$I =$ Identity Matrix