Question

If the matrix A is both symmetric and skew symmetric, then 

(A) A is a diagonal martix 

(B) A is a zero matrix 

(C) A is a square matrix 

(D) None of these

Answer 1

Answer is (B)

Let A be a square matrix such that A is both symmetric & skewsymmetric 

⇒ A’ = A – (i) & A’ = – A -(ii) 

⇒ A + A = 0 from (i) & (ii) 

2A = 0 

⇒ A = 0