Give a basis and the dimension of each of the following vector spaces...

(a) The space of 3 × 3 matrices which are invarient under a 90-degree clockwise rotation; that is, the matrices satisfying

$\displaystyle \begin{pmatrix} a&b&c\\d&e&f\\g&h&i\end{pmatrix} = \begin{pmatrix} g&d&a\\h&e&b\\i&f&c\end{pmatrix} $

(b) The space of polynomials in $\displaystyle P_n(\mathbb{R}) (n\geq 2) $ which are divisible by $\displaystyle x^2 +1 $. (i.e. they can be written as the product of $\displaystyle x^2 + 1 $ with another polynomial).