If matrix A is skew symmetric, then which of the following statements is not correct?
(a) B'AB is a skew symmetric
(b) A² is symmetric
(c) KA is skew symmetric
(d) AA' is skew symmetric
Answers
Answered by
3
Answer:
C=(A+B)
−1
(A−B),
⇒(A+B)C=(A+B)(A+B)
−1
(A−B)
⇒(A+B)C=A−B (1)
C
T
=(A−B)
T
((A+B)
−1
)
T
=(A+B)((A+B)
T
)
−1
as A is symmetric and B in anti-symmetric matrices.
{as∣A+B∣
=0⇒∣(A+B)
T
∣
=0⇒∣A−B∣
=0}
=(A+B)(A−B)
−1
(2)
From (1) and (2), we get
C
T
(A+B)C
=(A+B)(A−B)
−1
(A−B)
=(A+B) (3)
Taking transpose in (3), we get
C
T
(A+B)
T
(C
T
)
T
=(A+B)
T
C
T
(A−B)C=A−B
Adding (3) and (4) we get
C
T
[A+B+A−B]C=2A
C
T
AC=A
Similar questions