Show that the linear map $\displaystyle T:\wp_2 \to \wp_2$ defined by $\displaystyle T(\alpha_0+\alpha_1 x+\alpha_2x^2)=(\alpha_0+\alpha_1)+(\alpha_1+2\alp ha_2)x+(\alpha_0+\alpha_1+3\alpha_2)x^2$ is non-singular and find its inverse.

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