Question

Whats the general representation for above figure?

a) a+b = b+a

b) ab =ba

c) a-b =b-a

d) None of these​

Answer 1

Answer:

If A and B are symmetric matrices and AB = BA , then A^-1B is a

Answer 2

Answer:

b) ab=ba

Step-by-step explanation:

We have AB=BA=B

′

A

′

=(AB)

′

⇒AB is symmetric.

Also, ABA

−1

=BAA

−1

=B(∵AB=BA)

⇒A

−1

ABA

−1

=A

−1

B⇒BA

−1

=A

−1

B

Therefore, (A

−1

B)

′

=(BA

−1

)=(A

−1

)

′

B

′

=A

′

B [∵A

−1

and B are symmetric ]

Thus, the matrix A

−1

B is symmetric.