Question

for any square matrix with a real no. entries prove that A+A' is a symmetric matrix and A-A' is a skew symmetric matrix​

Answer 1

Answer:

Consider (A + A')'

= (A)' + (A')'

= A' + A

= A + A'

Hence, A + A' is symmetric.

Consider (A - A')'

= (A)' - (A')'

= A' - A

= -(A - A')

Hence, A - A' is skew symmetric.