Fill in the blanks in each of the If A is symmetric matrix, then B’AB is _______.

Question

Philoid · Accepted Answer

B’AB is a symmetric matrix.

Proof:

Given A is symmetric matrix

⇒ A’=A ..(1)

Now in B’AB,

Let AB=C ..(2)

⇒ B’AB=B’C

Now Using Property (AB)’=B’A’

⇒ (B’C)’=C’(B’)’ (As (B’)’=B)

⇒ C’(B’)’=C’B

⇒ C’B=(AB)’B (Using Property (AB)’=B’A’)

⇒ (AB)’B=B’A’B (Using (1))

⇒ B’A’B= B’AB

⇒ Hence (B’AB)’= B’AB