Linear transformation $ R^3 \to R^3$

Question

Let $T:R^3 \to R^3$ be the linear transformation of projection onto $x_1x_2$-plane. What is the linear transformation one obtains when you compose $T$ with itself?

I think $x_1x_2$ means projecting onto a two dimensional $XY$ plane. But what does it mean to compose $T$ with itself? is it the composition of $T$? Then I assume the composition of a linear transformation should be $R^3$ as well, since $T$ is not specified here, I am a little confused whether $T$'s composition is itself?

Any explanation would be appreciated thanks.

Answer 1

If $T(x_1,x_2,x_3)=(x_1,x_2,0)$ then $(T \circ T)(x_1,x_2,x_3)=T(x_1,x_2,0)=(x_1,x_2,0)$, hence $T \circ T=T$.