Linear Algebra - Matrices

Let $M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}$ be a $2 \times 2$ matrix, where $\theta = \frac{2\pi}{5}$, and $I_2 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$. Which o...

Let M = (I_n - (1/n)11^T) be a matrix, where 1 = (1,1,1, ...,1)^T ∈ R^n and I_n is the identity matrix of order n. Which of the following options is/are correct?