Q. 805.0( 1 Vote )
Fill 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 ______.
Answer :
This is only possible if A and B commute.
Proof:
Given A and B are symmetric matrices,
⇒ A’=A ..(1)
⇒ B’=B ..(2)
Let AB is a Symmetric matrix:-
⇒ (AB)’=AB
Using Property (AB)’=B’A’
⇒ B’A’=AB
⇒ Now using (1) and (2)
⇒ BA=AB
Hence A and B matrix commute.
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 A2 is a _________.
Mathematics - ExemplarIf 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 - ExemplarExpress the following matrix as the sum of a symmetric and skew-symmetric matrix, and verify your result:
Fill in the blanks in each of the
If A is symmetric matrix, then B’AB is _______.
Mathematics - Exemplar