Does there exist $T \in L(\Bbb R^6) \setminus \{0\}$ such that $\text {Im}\ (T) = \text {Ker}\ (T)\ $?

Question

Does there exist $T \in L(\Bbb R^6) \setminus \{0\}$ such that $\text {Im}\ (T) = \text {Ker}\ (T)\ $?

My attempt $:$ I take $T : \Bbb R^6 \longrightarrow \Bbb R^6$ defined by $T(x_1,x_2,x_3,x_4,x_5,x_6) = (x_4,x_5,x_6,0,0,0),\ $ $(x_1,x_2,x_3,x_4,x_5,x_6) \in \Bbb R^6.$ Then indeed we have $\text {Im}\ (T) = \text {Ker}\ (T).$ Am I right? Please check it.

Thanks for reading.