# Is an unspecified matrix invertible?

1. Jan 21, 2015

### Chillguy

1. The problem statement, all variables and given/known data
Let T be the unique linear operator on C3 for which $$T_{\epsilon1}=(1,0,i), T_{\epsilon2}=(0,1,1), T_{\epsilon3}=(i,1,0).$$
Is T invertible?
2. Relevant equations
If we show T is non singular or T is onto, then this would imply T is invertible.

3. The attempt at a solution
I don't really know where to start, I thought about trying to brute force solve the matrix T but I am quite sure there is a more elegant way and hoping someone can give me a kick in that direction.

2. Jan 21, 2015

### Stephen Tashi

Assuming the scalars for this vector space are the complex numbers, I think $Te_1$ is a linear combination of $Te_2$ and $Te_3$. If that's correct then you can show that T maps a 3-D space to a 2-D space.