Question

If a matrix A is both symmetric and skew-symmetric, then 

A. A is a diagonal matrix 

B. A is a zero matrix 

C. A is a scalar matrix 

D. A is a square matrix

Answer 1

(B). A is a zero matrix

If a matrix A is both symmetric and skew-symmetric, 

A’ = A & A’ = - A 

Comparing both the equations, 

A = - A 

A + A = 0 

2A = 0 

A = 0

then A is a zero matrix. 

Option (B) is the answer.