# How do you find the inverse of A=((1, 3, -1), (2, 5, 1), (1, 4, -4))?

Mar 21, 2016

The inverse of $A$, ${A}^{-} 1$ does not exist because the $\det A = 0$

#### Explanation:

The Inverse of $A$ is ${A}^{-} 1$ such that $A \cdot {A}^{1} = I$
Where I is the identity matrix with
a_(i,j) = 1 AA-> i=j; 0 otherwise
Quickly check for the determination to check for the existence of ${A}^{-} 1$
$\det A = 1 \left[\begin{matrix}5 & 1 \\ 4 & - 4\end{matrix}\right] - 3 \left[\begin{matrix}2 & 1 \\ 1 & - 4\end{matrix}\right] - \left[\begin{matrix}2 & 5 \\ 1 & 4\end{matrix}\right]$
$\det A = \left(- 20 - 4\right) - 3 \left(- 8 - 1\right) - \left(8 - 5\right) = 0$
With $\det A = 0$ the inverse of $A$, ${A}^{-} 1$ does not exist