What is an eigenvalue of a matrix $A$ ? What is the eigenspace corresponding to an eigenvalue $\lambda$ of $A$ ?

Consider the matrix

$$A=\left(\begin{array}{cccc} a a & a b & a c & a d \\ b a & b b & b c & b d \\ c a & c b & c c & c d \\ d a & d b & d c & d d \end{array}\right)$$

for $(a, b, c, d) \in \mathbb{R}^{4}$ a non-zero vector. Show that $A$ has rank 1 . Find the eigenvalues of $A$ and describe the corresponding eigenspaces. Is $A$ diagonalisable?