# How do you find the inverse of A=((1, -1, 0), (0, 1, 0), (0, 0, 1))?

Jul 16, 2016

${A}^{- 1} = \left(\begin{matrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right)$

#### Explanation:

${A}^{- 1} = \left(\begin{matrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right)$

Notice the effect of multiplying:

$A \left(\begin{matrix}a \\ b \\ c\end{matrix}\right) = \left(\begin{matrix}1 & - 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right) \left(\begin{matrix}a \\ b \\ c\end{matrix}\right) = \left(\begin{matrix}a - b \\ b \\ c\end{matrix}\right)$

To reverse the effect of subtracting $b$ from $a$ we need to add it. So all we need to do to form the inverse of $A$ is to reverse the sign of the off diagonal $- 1$.