Let-A-and-B-is-3-3-matrix-of-equal-number-where-A-symmetric-matrix-B-skew-symmetric-matrix-and-the-relation-A-B-A-B-A-B-A-B-then-the-value-of-k-AB-T-1-k-AB-a-1-

Question Number 19589 by gourav~ last updated on 13/Aug/17

L e t A a n d B i s 3 \times 3 m a t r i x o f e q u a l n u m b e r

w h e r e A = s y m m e t r i c m a t r i x

\dots . B = s k e w s y m m e t r i c m a t r i x

a n d t h e r e l a t i o n \dots (A + B) (A - B) = (A - B) (A + B)

t h e n . . t h e v a l u e o f . . \dots k

{(A B)}^{T} = {(- 1)}^{k} (A B)

(a) - 1 (c) 2

(b) 1 (d) 3

Answered by dioph last updated on 15/Aug/17

A^{2} - A B + B A - B^{2} = A^{2} + A B - B A + B^{2}

2 A B = 2 B A

A B = B A

{(A B)}^{T} = {(B A)}^{T}

{(A B)}^{T} = A^{T} B^{T}

{(A B)}^{T} = A (- B)

{(A B)}^{T} = (- 1) (A B)

Facebook Tweet Pin