Fewpal
0 votes
9 views
in Matrices by (49.6k points)
closed by

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

1 Answer

+1 vote
by (29.2k points)
selected by
 
Best answer

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

Given, B is a skew-symmetric matrix.

∴ B = -B’

Let C = A’ BA …(1)

We have to prove C is skew-symmetric.

To prove: C = -C’

As C’ = (A’BA)’

We know that: (AB)’ = B’A’

⇒ C’ = (A’BA)’ = A’B’(A’)’

⇒ C’ = A’B’A {∵ (A’)’ = A}

⇒ C’ = A’(-B)A

⇒ C’ = -A’BA …(2)

From equation 1 and 2:

We have,

C’ = -C

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

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...