Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A’ BA is skew symmetric.

If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A’ BA is skew symmetric.

Answers (1)

A matrix is said to be skew-symmetric if A = -A’

Given, B is a skew-symmetric matrix.

$ \therefore $ B = -B'

Let C = A'BA $ \ldots $ (1)

We have to prove C is skew-symmetric.

To prove: C = -C’

As C = A'BA $ \ldots $ (1)

We know that: (AB)’ = B’A’

\\$ \Rightarrow $ C' = (A'BA)' = A'B'(A')' \\$ \Rightarrow $ C' = A'B'A $ \{ $ $\because$ (A')' = A$ \} $ \\$ \Rightarrow $ C' = A'(-B)A \\$ \Rightarrow $ C' = -A'BA $ \ldots $ (2)

From equation 1 and 2:

We get,

C’ = -C

Thus, we say that C = A’ BA is a skew-symmetric matrix.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question