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if a and b are symmetric matrices, then aba is

Let A=A^T and B=B^T for suitably defined matrices A and B. Share with your friends. Then A*B=(A*B)^T=B^T*A^T=B*A. A matrix is symmetric if and only if it is equal to its transpose, ie 1 $\begingroup$ Closed. 1. a-symmetric. Given A and B are symmetric matrices, then (AB)^T = B^T A^T = BA. 2. This holds for some specific matrices, but it … Example 27 If A and B are symmetric matrixes of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA. Viewed 22 times -1. 0 ; View Full Answer a-symmetric matrix. 1. Given A is a symmetric matrix, then A^2 = AA^T, so A^2 must also be a symmetric matrix. If A and B are n×n matrices and if A is invertible, then ABA−1=B. If A is non-singular and diagonal, then A^-1 is also non singular and diagonal. Check Answer a Determine if the statements are true or false. False; ABA is symmetric, but AB is not symmertic. If A and B are symmetric and commute, then which of the following is/are symmetric? If A is row equivalent to B, then the systems Ax=0 and Bx=0 have the same solution. MEDIUM. If A is a skew-symmetric matrix and n is a positive integer, then … This question has multiple correct options. AB = BA) i. If A = [1 0 2 3 ] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then find B. if A and B are symmetric matrices, then ABA is. (a) Give an example to show that if A and B are symmetric n × n matrices, then AB need not be symmetric. Active today. Share 1. it is symmetric matrix as (ABA)' = (A)'(AB)' = AB'A =ABA. hence it is symmetric matrix. (b) Prove that if A and B are symmetric n × n matrices, then AB is symmetric … It is not currently accepting answers. Suppose that A*B=(A*B)^T. A’ = A B’ = B We need to show AB is symmetric if and only if A & B commute (i.e. ... Let A and B be two nonsingular square matrices, A T and B T are the transpose matrices A and B, respectively, then which of the following are correct? c-diagonal. Given A & B are symmetric matrix i.e. Click here👆to get an answer to your question ️ Let A and B be two symmetric matrices of order 3.Statement - 1: A(BA) and (AB)A are symmetric matrices.Statement - 2: AB is symmetric matrix if matrix multiplication of A and B is commutative. This question does not meet Mathematics Stack Exchange guidelines. VITEEE 2016: If A and B are matrices and B = ABA-1 then the value of (A + B) (A - B) is (A) A2 + B2 (B) A2 - B2 (C) A + B (D) A - B . If A and B are real symmetric matrices of size n×n, then (AB)T=BA. A positive definite matrix is always non singular. If A and B are symmetric matrices then AB= (a)BA (b)A'B' (c)B'A' (d) (a)and(c) [closed] Ask Question Asked today. View Answer. In particular, A*B=B*A. View Answer. Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website! True. If A and B are symmetric matrices, then AB and ABA are symmetric as well. d-scalar. If A and B are symmetric matrices of same order, prove that AB- BA is a symmetric matrix. A) (A^2 - B^2)^T = (A^2)^T - (B^2)^T = A^2 - B… b-skew-symmetric. View Answer. 3. If B is a skew-symmetric matrix, write whether the matrix (ABA) is symmetric or skew - 986779 4. Question 1006565: If A and B are symmetric matrices and if AB = BA, then AB is symmetric is this statement true or false and why? If, for some matrix A and some vectors x and b we have Ax=b, then b is a linear combination of the columns of A.

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