Let ω be a complex cube root of unity with ω ≠ 1 and P = [p_ij] be a n × n matrix with p_ij = ω^{i + j}. Then P²≠ 0, when n =

If P is a matrix such that, where is the transpose of P and I is the identity matrix, then there exists a column matrix such that

Let M be a matrix satisfying

and

Then the sum of the diagonal entries of M is

The number of matrices in A is

Match the statements/ Expressions in Column I with the Statements/ Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the matrix given in the ORS.

	Column I		Column II
(A)	The minimum value of	(p)	0
(B)	Let A and B be matrices of real number, where A is symmetric, B is skew − symmetric and (A +B)(A − B) = (A − B) (A + B). If AB, where (AB)t is the transpose of the matrix AB, then the possible values of k are	(q)	1
(C)	Let a =. An integer k satisfying , must be less than	(r)	2
(D)	If , then the possible values of are	(s)	3

The value of $\left[3 2 0 \right] \mathrm{U} \left[\begin{array}{c}3\\ 2\\ 0\end{array}\right]$ is