Share 1. it is symmetric matrix as (ABA)' = (A)'(AB)' = AB'A =ABA. MEDIUM. Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website! Let A=A^T and B=B^T for suitably defined matrices A and B. If A is a skew-symmetric matrix and n is a positive integer, then â¦ Given A & B are symmetric matrix i.e. If A and B are symmetric matrices of same order, prove that AB- BA is a symmetric matrix. 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? d-scalar. 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. (a) Give an example to show that if A and B are symmetric n × n matrices, then AB need not be symmetric. If A is row equivalent to B, then the systems Ax=0 and Bx=0 have the same solution. It is not currently accepting answers. Click hereðto get an answer to your question ï¸ 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. 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. c-diagonal. 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. A) (A^2 - B^2)^T = (A^2)^T - (B^2)^T = A^2 - Bâ¦ AB = BA) i. 2. This question does not meet Mathematics Stack Exchange guidelines. In particular, A*B=B*A. 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 . ... 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? If A and B are symmetric matrices, then AB and ABA are symmetric as well. Given A and B are symmetric matrices, then (AB)^T = B^T A^T = BA. 1. (b) Prove that if A and B are symmetric n × n matrices, then AB is symmetric â¦ if A and B are symmetric matrices, then ABA is. hence it is symmetric matrix. A positive definite matrix is always non singular. This question has multiple correct options. Check Answer a 0 ; View Full Answer a-symmetric matrix. Viewed 22 times -1. View Answer. b-skew-symmetric. False; ABA is symmetric, but AB is not symmertic. If A is non-singular and diagonal, then A^-1 is also non singular and diagonal. View Answer. 1 $\begingroup$ Closed. If A and B are n×n matrices and if A is invertible, then ABAâ1=B. Given A is a symmetric matrix, then A^2 = AA^T, so A^2 must also be a symmetric matrix. 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. Suppose that A*B=(A*B)^T. Share with your friends. Active today. Then A*B=(A*B)^T=B^T*A^T=B*A. 3. True. View Answer. If A and B are symmetric and commute, then which of the following is/are symmetric? If A and B are real symmetric matrices of size n×n, then (AB)T=BA. 4. If B is a skew-symmetric matrix, write whether the matrix (ABA) is symmetric or skew - 986779 Aâ = A Bâ = B We need to show AB is symmetric if and only if A & B commute (i.e. This holds for some specific matrices, but it â¦ a-symmetric. Determine if the statements are true or false. 1. A matrix is symmetric if and only if it is equal to its transpose, ie Then A^2 = AA^T, so A^2 must also be A symmetric.. Diagonal, then which of the following is/are symmetric AB is not symmertic AB not! Of the following is/are symmetric Let A=A^T and B=B^T for suitably defined matrices and... Systems Ax=0 and Bx=0 have the same solution symmetric n × n matrices, A^2! 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