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 non-singular matrix A is symmetric ,show that A^(-1) is also symmetric

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

Write a 2xx2 matrix which is both symmetric and skew-symmetric.

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)

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

If A is a non-singular symmetric matrix, write whether A^(-1) is symmetric or skew-symmetric.

If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

Write a square matrix of order 2, which is both symmetric and skew symmetric.

Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric iff A^2=(A^T)^2 .

Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric if A^2=(A^T)^2