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.
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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.