If `Aa n dB` are symmetric and commute, then which of the following is/are symmetric? `A^(-1)B` b. `A B^(-1)` c. `A^(-1)B^(-1)` d. none of these

If Ais symmetric and B is skew-symmetric matrix, then which of the following is/are CORRECT ?

If A and B are symmetric matrices of order n,where (A ne B) ,then:

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? B^T A B is symmetric matrix if A is symmetric B^T A B is symmetric matrix if B is symmetric B^T A B is skew-symmetric matrix for every matrix A B^T A B is skew-symmetric matrix if A is skew-symmetric

If A and B are two non singular matrices and both are symmetric and commute each other, then

If alphaa n dbeta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a. A_(n+1)=a A_n+b A_(n-1) b. A_(n+1)=b A_(n-1)+a A_n c. A_(n+1)=a A_n-b A_(n-1) d. A_(n+1)=b A_(n-1)-a A_n

If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n dY=A B-B A ,t h e n(X Y)^T is equal to X Y b. Y X c. -Y X d. none of these

If a and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

If Aa n dB are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e nA^(-1)B^(r-1)A=A^(-1)B^(-1)A= I b. 2I c. O d. -I

If both A-1/2Ia n dA+1/2 are orthogonal matices, then (a) A is orthogonal (b) A is skew-symmetric matrix of even order (c) A^2=3/4I (d)none of these