Question

If P and Q are symmetric matrices of the same order then PQ-QP is (A) zero matrix (B) identity matrix (C) skew symmetric matrix (C) symmetric matrix

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12th

Maths

Matrices

Multiplication of Matrices and their Properties

P- symmetric matrix, Q- ske...

MATHS

Asked on December 20, 2019 byBhavinya Chakravarty

P- symmetric matrix, Q- skew symmetric matrix, P and Q are square matrice of same order, then what type of a matrix is PQ-QP

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ANSWER

The product of a symmetric matrix and a skew symmetric matrix is skew symmetric matrix

The product of a skew symmetric matrix and a symmetric matrix is skew symmetric matrix

So(PQ)=(−QP)T and QP=(−PQ)T Hence

PQ−QP=−−(QP)T+(PQ)T=(PQ−QP)T

Proving that PQ−QP is symmetric.