Question:
If A and B are symmetric matrices of the same order, then
If A and B are symmetric matrices of the same order, then
Updated On: Jul 6, 2022
- AB is a symmetric matrix
- A - B is a skew-symmetric matrix
- AB + BA is a symmetric matrix
- AB - BA is a symmetric matrix
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$\left(AB + BA\right)^{t} = \left(AB\right)^{t} + \left(BA\right)^{t} $
$ = B^{t} A^{t} + A^{t} B^{t} =BA + AB = AB + BA $
$ \left(\because A^{t} =A \, \text{and} \, B^{t} =B\right) $
Was this answer helpful?
0
0
Top Questions on Matrices
- If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:
- Which of the following statements is not correct?
- If A and B are two matrices such that AB is an identity matrix and the order of matrix B is \(3 \times 4\), then the order of matrix A is:
- If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:
- If \( B = \begin{bmatrix} 1 & 3 \\ 2 & \alpha \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( |A| = 2 \), then the value of \( \alpha \) is:
View More Questions
Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.