Endomorphism given on the vectors of a basis

Let $f:{\mathbb{R}}^3\to {\mathbb{R}}^3$ be the endomorphism such that

$$f(1,1,0)=(2,2,0),f(0,1,1)=(0,2,2),f(1,0,1)=(0,0,0).$$

Determine the eigenvalues and eigenspaces of $f$, determine whether $f$ is diagonalizable and write the matrix associated with $f$ with respect to the standard basis.