Question

Plz slove this question

Answer 1

i)consider AB-BA=P
P’=(AB-BA)’=(AB)’-(BA)’
=B’A’-A’B’................................. (1)

Since A and B are symmetric, A’=A and B’=B
Hence, (1) becomes:
BA-AB

Now consider -P
-P=-(AB-BA) = BA-AB

We see that P’=-P
Hence P(AB-BA) is skew symmetric



ii)consider AB+BA =Q
Q’=(AB+BA)’=(AB)’+(BA)’
=B'A'+A'B'
since A and B are symmetric A’=A and B'=B
Q=BA+AB=AB+BA

Hence, Q=Q’, therefore Q(AB+BA) is a symmetric matrix.