Let A = [(0, -2), (2, 0)]. If M and N are two matrices given by M = ΣA^2k, k ∈ (1, 10) and N = ΣA^2k-1 then MN^2 is

Question

Let A = \(\begin{bmatrix}0&-2\\2&0\end{bmatrix}\). If M and N are two matrices given by M = \(\sum\limits_{k=1}^{10}\)A^2k, and N = \(\sum\limits_{k=1}^{10}\)A^2k-1 then MN² is

(A) a non-identity symmetric matrix 

(B) a skew-symmetric matrix 

(C) neither symmetric nor skew-symmetric matrix 

(D) an identify matrix

Answer 1

Correct option is (A) a non-identity symmetric matrix

= λ A ⇒ skew symmetric

⇒ N² is symmetric matrix

⇒ MN² is non identity symmetric matrix