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 B=Aa n dB A=B , then which of the following is/are true? A is idempotent b. B is idempotent c. A^T is idempotent d. none of these

If positive quantities a,b,c are in H.P. , then which of the following is not true ? a. b gt (a+c)/(2) b. (1)/(a-b)-(1)/(b-c) gt 0 c. ac gt b^(2) d. none of these

If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, then which of the following is true? (a) f(x+1)=f(x) (b) f(x+3)=f(x) (c) f(x+2)=f(x) (d) None of these

Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following options are correct? (correct option may be more than one) (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric

If A is a matrix such that A^2+A+2I=Odot, the which of the following is/are true? (a) A is non-singular (b) A is symmetric (c) A cannot be skew-symmetric (d) A^(-1)=-1/2(A+I)

If A is an orthogonal matrix then A^(-1) equals a. A^T b. A c. A^2 d. none of these

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

If alpha and beta 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

In the expansion of (a+b)^(n) , if two consecutive terms are equal, then which of the following is/are always integer ? (a) ((n+1)b)/(a+b) (b) ((n+1)a)/(a+b) (c) (na)/(a-b) (d) (na)/(a+b)