Question:
If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$
If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$
Updated On: Jun 8, 2024
- BAB
- ABA
- ABAB
- $AB^{T}$
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The Correct Option is B
Solution and Explanation
Let$ P =(A B A)^{T}=A^{T} B^{T} A^{T} $
$ A =A^{T}, B=B^{T}=A B A $
$ A =A^{T}, B=B^{T}=A B A $
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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.