Let $T:\Bbb R^4\longrightarrow\Bbb R^4$ be a linear transformation satisfying $T^3+3T^2=4I$, where $I$ is the identity transformation. Then the linear transformations $S=T^4+3T^3-4I$ is
a). one-one but not onto.
b). onto but not one-one.
c). Invertible.
d). Non-invertible.
on solving i get $S=4T-4I$, but how does this suggest invertibilty? Also, Logically thinking option $a,b$, and $d$ are interlinked. So if only one choice is correct then i could simply say that yes option $c$ is correct. But can someone give the general aproach?