ISRO2011-36

Question

If $\text{A}$ and $\text{B}$ are square matrices with same order and $\text{A}$ is symmetric, then $\text{B}^{\text{T}}\text{AB}$ is

• A. Skew symmetric
• B. Symmetric
• C. Orthogonal
• D. Idempotent

Answer 1

If A is a Symmetric Matrix then A=A⊤        // Sign ⊤ Showing as Transpose

(B⊤AB)⊤ =B⊤A⊤B

it ia already given A=A⊤ So

B⊤AB

Answer : Symmetric

BTBTBT

Answer 2

We knows that ( A B )^T = B^T A^T  and  ( A^T )^T = A

Given A is Symmetric i.e. A = A^T

Now,

( B^T A B )^T = ( B^T A^T B ) = ( B^T A B )

Hence,Option(B)Symmetric is the correct choice.