Question

if p and q are invertible matrices of same order then adjoint QP equal to​

Answer 1

Answer:

Answer:

(PQ - QP ) is a Skew Symmetric Matrix

Step-by-step explanation:

Since:

P and Q Symmetric Matrices therefore

Transport of P = T(P) = P                  .....(1)

Transport of Q = T(Q) = Q               .....(2)

Now

Transport of (PQ -QP) = T( PQ - QP )  

Using the property of Transport   T(A-B)=T(A) - T(B)

T( PQ - QP ) = T(PQ) - T(QP)                            

Using again property of transport     T(AB) = T(B) T(A)

T(PQ) - T(QP) = T(Q) T(P) - T(P) T(Q)        ............(3)

Using Equations (1) and (2) in (3) we get

T(PQ) - T(QP) = QP - PQ

T(PQ) - T(QP) = - ( PQ - QP)                                  

SO  

Transport of (PQ - QP) = T( PQ - QP ) = - ( PQ - QP)

Which show that  

(PQ - QP ) is a Skew Symmetric Matrix.

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