Question:
If A, B are symmetric matrices of the same order then AB - BA is a
If A, B are symmetric matrices of the same order then AB - BA is a
Updated On: Jul 6, 2022
- Skew symmetric matrix
- Symmetric matrix
- Zero matrix
- Identity matrix.
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The Correct Option is A
Solution and Explanation
A and B are symmetric matrices $\Rightarrow \, A' = A$
$\Rightarrow \, B' = B $
Now $(AB - BA)' = (AB)' - (BA)'$
$= B'A' - A'B' = BA - AB$
$\because \, B' = B, A' = A = - (AB - BA)$
$ \Rightarrow \, (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.