Question:
If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?
If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?
Updated On: Jul 27, 2022
- $AB = BA$
- either of $A$ or $B$ is a zero matrix
- either of $A$ or $B$ is an identity matrix
- $A = B$
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The Correct Option is A
Solution and Explanation
$\because A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$
$\Rightarrow A^{2}-B^{2}=A^{2}-B^{2}+AB-BA$
$\Rightarrow AB=BA$
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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.
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