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If-A-is-a-square-matrix-of-order-3-then-A-A-T-2011-




Question Number 41321 by rahul 19 last updated on 05/Aug/18
If A is a square matrix of order 3, then   ∣(A−A^T )^(2011) ∣ = ?
IfAisasquarematrixoforder3,then(AAT)2011=?
Commented by rahul 19 last updated on 05/Aug/18
I ′m getting A−A^T  a skew symmetric   of order 3.  I wanted to know why (A−A^T )^(2011) will  also be a skew synmetric of order 3    !
ImgettingAATaskewsymmetricoforder3.Iwantedtoknowwhy(AAT)2011willalsobeaskewsynmetricoforder3!
Answered by MJS last updated on 05/Aug/18
 ((a,b,c),(d,e,f),(g,h,i) ) − ((a,d,g),(b,e,h),(c,f,i) ) = ((0,p,q),((−p),0,r),((−q),(−r),0) )   ((0,p,q),((−p),0,r),((−q),(−r),0) )^(2n−1) =  = ((0,((−1)^(n−1) p(p^2 +q^2 +r^2 )^(n−1) ),((−1)^(n−1) q(p^2 +q^2 +r^2 )^(n−1) )),(((−1)^n p(p^2 +q^2 +r^2 )^(n−1) ),0,((−1)^(n−1) r(p^2 +q^2 +r^2 )^(n−1) )),(((−1)^n q(p^2 +q^2 +r^2 )^(n−1) ),((−1)^n r(p^2 +q^2 +r^2 )^(n−1) ),0) )
(abcdefghi)(adgbehcfi)=(0pqp0rqr0)(0pqp0rqr0)2n1==(0(1)n1p(p2+q2+r2)n1(1)n1q(p2+q2+r2)n1(1)np(p2+q2+r2)n10(1)n1r(p2+q2+r2)n1(1)nq(p2+q2+r2)n1(1)nr(p2+q2+r2)n10)
Commented by rahul 19 last updated on 06/Aug/18
thanks sir ����

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