(B^T-B)A=0->B^T=B# which is an absurd. If A and B are symmetric matrices of the same order then (AB-BA) is always. Concept: Symmetric and Skew Symmetric Matrices. What is the meaning of the phrase invertible matrix? Directions (Q. If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA. If we multiply a symmetric matrix by a scalar, the result will be a symmetric matrix. C |A| D diagonal matrix. We have, Now consider AB - BA and by taking transpose of it, we get, =By taking negative in common we get, −(AB−BA), We know that a matrix is said to b skew symmetric matrix if A=−A, From the property of transpose of matrices. ; For integer , is symmetric if is symmetric. sequence is geometric and the next two numbers are –22 and 44. Give an example of a symmetric matrix order 3×3. AB is symmetric â AB = BA. Hence proved. If A and B are symmetric matrices, then find BA â 2AB . 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# if a and b are symmetric matrices then ab'-ba' is 