Math Help - Linear map

1. Linear map

Show that the linear map $T:\wp_2 \to \wp_2$ defined by $T(\alpha_0+\alpha_1 x+\alpha_2x^2)=(\alpha_0+\alpha_1)+(\alpha_1+2\alp ha_2)x+(\alpha_0+\alpha_1+\alpha_2)x^2$ is non-singular and find its inverse.

Show that the linear map $T:\wp_2 \to \wp_2$ defined by $T(\alpha_0+\alpha_1 x+\alpha_2x^2)=(\alpha_0+\alpha_1)+(\alpha_1+2\alp ha_2)x+(\alpha_0+\alpha_1+\alpha_2)x^2$ is non-singular and find its inverse.
2)Show that T is one-one and onto. Let F be the inverse map, then $T\circ F = \text{Id}$. So compute F directly from that.