# Finding the inverse of this matrix.

1. Mar 6, 2012

### Kuma

1. The problem statement, all variables and given/known data

Hi there I'm trying to solve this question:

2. Relevant equations

3. The attempt at a solution

I figured i should just multiply them together and show that you get the identity matrix, but I'm having trouble cancelling out some of the terms. I'm not sure if I should write them out in matrix form first or just do them as is?

2. Mar 7, 2012

### Staff: Mentor

I haven't worked this all the way through, but your idea of multiplying the two expressions seems like the way to go.

Here are a couple of tips that might be helpful. The 1n1n' expressions represent n x n matrices whose entries are all 1's.

The product 1n1n' * 1n1n' works out to be n * 1n1n', which you might need to prove by induction.

3. Mar 7, 2012

### Kuma

It says that 1n is a vector of 1's so shouldnt 11' = n?

4. Mar 7, 2012

### micromass

Staff Emeritus
They probably mean that $1_n$ is a column vector. Otherwise the dimensions wouldn't agree. Indeed: $(1-\rho)I$ would be a matrix and $1_n1_n^\prime$ would be a number, so you can't add them.

5. Mar 7, 2012

### Staff: Mentor

I agree with micromass. 1n has to be a column vector.