# Math Help - Inverse

1. ## Inverse

Find the inverse of a nxn matrix defined as:

$a_{ij}=\begin{cases}1, & \text{if} \ \ i\leq j\\0, & \text{if} \ \ i>j\end{cases}$

If A is 2x2, the matrix is $\begin{bmatrix}1&-1\\0&1\end{bmatrix}$

If A is 3x3, $\begin{bmatrix}1&-1&0\\0&1&-1\\0&0&1\end{bmatrix}$

I am not seeing a recognizable pattern.

I can see this much

$a^{-1}_{ij}=\begin{cases}1, & \text{if} \ \ i= j\\0, & \text{if} \ \ i>j\\ \text{potential another case here}\end{cases}$

2. ## Re: Inverse

$a^{-1}_{ij}=\begin{cases}1, & \text{if} \ \ i= j\\-1, & \text{if} \ \ i=j-1\\ \text{0 elsewhere}\end{cases}$