$T:R^3\to R^3$
$T(x,y,z)=(x+3y+2z,3x+4y+z,2x+y-z)$
I want to find the dimension of the Null Space of $T^3$
Here Nullity of $T$ is not $0$, so I can't say anything directly about the nullity of $T^3$
Normally for the nullity of T, I would form the matrix of transformation by take the image of the standard basis of $R^3$, then row reduce to calculate the rank and use the dimension theorem.
But doing the same for $T^3$ is turning out to be hefty task and I am looking for a easier way.