Let $A$ be a $2 \times 2$ matrix as given.

$$A=\left[\begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]$$

What are the eigenvalues of the matrix $A^{13}$ ?

Let A be an n × n matrix over the set of all real numbers ℝ. Let B be a matrix obtained from A by swapping two rows. Which of the following statements is/are TRUE?

Let A be any n x m matrix, where m > n. Which of the following statements is/are TRUE about the system of linear equations Ax = 0?

Which one of the following is the closed form for the generating function of the sequence (a_n}_{n $$\ge$$ 0} defined below?

$${a_n} = \left\{ {\matrix{ {n + 1,} & {n\,is\,odd} \cr {1,} & {otherwise} \cr } } \right.$$