Q. 1005.0( 1 Vote )

# Which of the following statements are True or False

If A is skew symmetric matrix, then A^{2} is a symmetric matrix.

Answer :

True

For skew symmetric matrix A’=-A

⇒ (A^{2})’=(AA)’=A’A’

⇒ A’A’=(-A)(-A)=A^{2}

⇒ (A^{2})’=A^{2} (symmetric matrix)

Rate this question :

Which of the following statements are True or False

AA’ is always a symmetric matrix for any square matrix A.

Mathematics - ExemplarWhich of the following statements are True or False

AA’ is always a symmetric matrix for any square matrix A.

Mathematics - ExemplarFill in the blanks in each of the

Sum of two skew symmetric matrices is always _______ matrix.

Mathematics - ExemplarFill in the blanks in each of the

If A and B are symmetric matrices, then

(i) AB – BA is a _________.

(ii) BA – 2AB is a _________.

Mathematics - ExemplarFill in the blanks in each of the

If A is a skew symmetric matrix, then A^{2} is a _________.

If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A’ BA is skew symmetric.

Mathematics - ExemplarFill in the blanks in each of the

If A is symmetric matrix, then B’AB is _______.

Mathematics - ExemplarFill in the blanks in each of the

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.

Mathematics - ExemplarShow that all the diagonal elements of a skew-symmetric matrix are zero.

Mathematics - Board Papers