Question

If A is a square matrix then (A-A ’) is 

A. A null matrix 

B. An identity matrix 

C. A symmetric matrix 

D. A skew-symmetric matrix

Answer 1

Let X = A-A’ 

X’ = (A-A’)’ 

= A’ - (A’)’ 

=A’ – A 

= -(A – A’) 

= -X 

Therefore (A-A’) is skew symmetric matrix.