Matrix of a linear transformation in a given basis

Let

$$T=\begin{pmatrix}1&0&0\\1&1&0\\1&1&1\end{pmatrix}.$$

Then the matrix of the linear transformation $T:\mathbb R^3\to\mathbb R^3$ defined by $T(X)=TX$; with respect to the basis $B=\left\{\begin{pmatrix}1\\0\\0\end{pmatrix},\begin{pmatrix}1\\1\\0\end{pmatrix},\begin{pmatrix}1\\1\\1\end{pmatrix}\right\}$ over $\mathbb R$ is