Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

For 3xx3 matrices M \ a n d \ N , which of the following statement (s) is (are) NOT correct ? Statement - I : N^T M N is symmetric or skew-symmetric, according as M is symmetric or skew-symmetric. Statement - II : M N-N M is skew-symmetric for all symmetric matrices Ma n dN . Statement - III : M N is symmetric for all symmetric matrices M a n dN . Statement - IV : (a d jM)(a d jN)=a d j(M N) for all invertible matrices Ma n dN .

If the matrix A is both symmetric and skew symmetric then

If the matrix A is both symmetric and skew-symmetricx then____

If A is symmetric as well as skew-symmetric matrix, then A is

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_1, A_2, , A_(2n-1) are n skew-symmetric matrices of same order, then B=sum_(r=1)^n(2r-1)(A^(2r-1))^(2r-1) will be (a) symmetric (b) skew-symmetric (c) neither symmetric nor skew-symmetric (d)data not adequate

Prove that inverse of a skew-symmetric matrix (if it exists) is skew-symmetric.

The inverse of a skew-symmetric matrix of odd order a. is a symmetric matrix b. is a skew-symmetric c. is a diagonal matrix d. does not exist

If A and B are symmetric matrices, prove that AB-BA is a skew symmetric matrix.

The inverse of a diagonal matrix is a. a diagonal matrix b. a skew symmetric matrix c. a symmetric matrix d. none of these