Let $T : V \to V$ be a linear transformation such that $T^2 = 0$. Choose the correct statement(s). Let $T : V \to V$ be a linear transformation such that $T^2 = 0$. Then, choose the correct statement(s). $a$. Kernel of $T$ is a subset of image of $T$ $b$. Image of $T$ is a subset of kernel of $T$. $c$ $T$ is $0$ linear transformation. $d$. $T$ is non singular linear transformation. $c$ and $d$ are incorrect. I'm confused between $a$ and $b$. I took an example of a nill potent matrix of index $2$, and option $b$ seems to be true. But I'm not sure. How to select from $a$ and $b?$

$T(T(v))=0$ and so $T(v)\in$ Ker$(T)$. Hence (b) is true.

Consider (a) when all $T(v)=0$. Then the kernel is all of $V$ whilst the image is only {$0$}. So (a) is not true in general.