If A,B are symmetric matrices of same order,then AB−BA is a
- Skew symmetric matrix
- Symmetric matrix
- Zero matrix
- Identity matrix
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.
Top Questions on Matrices
Let
\( A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix} \)
and \(|2A|^3 = 2^{21}\) where \(\alpha, \beta \in \mathbb{Z}\). Then a value of \(\alpha\) is:
- If \(A = \begin{bmatrix} 3 & 2 \\ -1 & 1 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} -1 & 0 \\ 2 & 5 \\ 3 & 4 \end{bmatrix},\)then \((BA)^T\) is equal to:
- If \( A = \begin{bmatrix} K & 4 \\ 4 & K \end{bmatrix} \) and \( |A^3| = 729 \), then the value of \( K^8 \) is:
- Let $A$ be a matrix such that $A^2 = I$, where $I$ is an identity matrix. Then $(I + A)^4 - 8A$ is equal to:
- Let $A = I_2 - MM^T$, where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M = I_1$ holds. If $\lambda$ is a real number such that the relation $AX = \lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:
Questions Asked in CBSE CLASS XII exam
What is the Planning Process?
- CBSE CLASS XII - 2023
- Planning process steps
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)
- CBSE CLASS XII - 2021
- Determinants
- Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).
- CBSE CLASS XII - 2021
- Three Dimensional Geometry
- Find the integrals of the function: \(cos\, 2x\, cos\, 4x\, cos\, 6x\)
- CBSE CLASS XII
- integral
Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2 }. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
- CBSE CLASS XII
- Relations and Functions
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.