Question:
If A,B are symmetric matrices of same order,then AB−BA is a
If A,B are symmetric matrices of same order,then AB−BA is a
Updated On: Sep 30, 2023
- Skew symmetric matrix
- Symmetric matrix
- Zero matrix
- Identity matrix
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is(A): Skew symmetric matrix.
A and B are symmetric matrices, therefore, we have:
A=A and B=B...(1)
consider
(AB-BA)=(AB)-(BA) [(A-B)=A-B]
=BA-AB[(AB)=BA]
=BA-AB [by(1)]
=-(AB-BA)
Therefore (AB-BA)=-(AB-BA)
Thus,
(AB−BA) is a skew-symmetric matrix.
Was this answer helpful?
1
0
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix} \). The determinant of \( A^3 \) is:
- Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.
- The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :
- If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
- If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :
View More Questions
Questions Asked in CBSE CLASS XII exam
- ‘But the game he is watching so intently is out of his reach.’ What are the factors that have made their game inaccessible to Saheb? (Lost Spring)
- CBSE CLASS XII - 2025
- Literature
- The basic scheme of the essential steps involved in the process of recombinant DNA technology is summarised below in the form of a flow diagram. Study the given flow diagram and answer the questions that follow: \begin{center} Step-1 \quad Plasmid DNA (cut using Restriction Enzyme EcoR I) \quad + \quad Foreign DNA (cut using Restriction Enzyme EcoR I)
$\downarrow$
DNA ligase
$\downarrow$
Step-2 \quad Recombinant DNA molecule
$\downarrow$
Step-3 \quad Transfer of recombinant DNA molecule to the host cell
$\downarrow$
Step-4 \quad Replication of recombinant DNA molecule in the host cell \end{center} (a) Name the specific enzyme that might have been used to make the multiple copies of foreign DNA before undergoing Step-1 of the process.
(b) How does the use of restriction enzyme EcoR I in Step-1 facilitate the action of DNA ligase to form the recombinant DNA molecule? Explain.
(c) Name the most commonly used host in the above process.- CBSE CLASS XII - 2025
- Biotechnology
- Draft an invitation card on behalf of the Principal of J.B. Bhatia Public School for the launch of ‘Yoga for Life’ programme in the school. Mention a compelling highlight of the programme along with other necessary details.
- CBSE CLASS XII - 2025
- Letter Writing
- What is the difference between CRS and GDS?
- CBSE CLASS XII - 2025
- Hotel Operations
- What is the significance of reservation to the guest?
- CBSE CLASS XII - 2025
- Hotel Operations
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.