Question

Let A, B, C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements

(S1) A¹³B²⁶ – B²⁶A¹³ is symmetric

(S2) A²⁶C¹³ – C¹³A²⁶ is symmetric Then,

(1) Only S2 is true

(2) Only S1 is true

(3) Both S1 and S2 are false

(4) Both S1 and S2 are true

Answer 1

Correct option is (1) Only S2 is true

Answer 2

Correct option is (1) Only S2 is true

M is skew symmetric

N is symmetric

Only S2 is true 

Answer 3

Correct option is (1) Only S2 is true

P is skew-symmetric matrix ⇒ S1 is false

⇒ QT = Q ⇒ Q is symmetric matrix ⇒ S2 is true