Let $T:\mathbb R^7 \longrightarrow \mathbb R^7$ be the linear transformation given by $$ T(x_1, x_2, x_3, x_4 ,x_5, x_6, x_7) = (x_7, x_6, x_5 ,x_4 ,x_3 ,x_2 ,x_1) $$ Which of the following statements are true?
a. Determinant of $T$ is $1$
b. Basis of $\mathbb R^7$ w.r.t. $T$ is a diagonal matrix
c. $T^7 =I$
d. Smallest $n$ s.t. $T^n =I$ is even.
I am stuck on this problem and don't know where to begin. Can anyone help me please?