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

Show that if A and B are symmetric and commute ,then AB^(-1)

If A and B are symmetric matrices, then write the condition for which A B is also symmetric.

Show that if A and B are symmetric and commute ,then A^(-1) B^(-1) are symmetric .

Which of the following is point symmetric? (a) Equilateral triangle (b) Trapezium (c) Rectangle (d) None of these

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 P and Q are symmetric matrices and PQ=QP then which of the following is/are true (A) QP^-1=P^-1Q (B) PQ is skew symmetric (C) P^-1Q is symmetric (D) both (a) and (c)

If A and B are symmetric matrices, then show that A B is symmetric if A B=B A i.e. A and B commute.

If A is a square matrix which of the following is not as symmetric matrix? (A) A-A\' (B) A+A\' (C) A A\' (D) A+B

If A and B are invertible matrices, which of the following statement is not correct. a d j\ A=|A|A^(-1) (b) det(A^(-1))=(detA)^(-1) (c) (A+B)^(-1)=A^(-1)+B^(-1) (d) (A B)^(-1)=B^(-1)A^(-1)

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? (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