1. ## Matrix Problem

The square matrix X is such that X^3 = 0. Show that the inverse of the matrix (I - X) is I + X + X^2.

2. $(i-x)(i+x+x^{2}) = i^{2} + ix +ix^{2} - xi -x^{2} - x^{3}$

$= i + x + x^{2} - x - x^{2} - x^{3} = i - 0 = i$

EDIT : I don't why it keeps making it lowercase.

3. You should probably also show that (I+X+X^2)(I-X) = I

4. Originally Posted by Random Variable
EDIT : I don't why it keeps making it lowercase.
Type $$\mathcal{X}$$ to get $\mathcal{X}$.

5. Originally Posted by Plato
Type $$\mathcal{X}$$ to get $\mathcal{X}$.
Why is it converted to lowercase sometimes?

I guess I could also use $\text{X}$