Question:
For any square matrix $A, AA^T$ is a
For any square matrix $A, AA^T$ is a
Updated On: Jul 6, 2022
- unit matrix
- symmetric matrix
- skew-symmetric matrix
- diagonal matrix
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The Correct Option is B
Solution and Explanation
We have, $(AA^T) ^T = (A^T) ^ TA^T= AA^T $
$\therefore AA^T$is a 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.
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- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.