(B) Let $B = AA^T$. To check if $B$ is symmetric,we find its transpose $B^T$. $B^T = (AA^T)^T$. Using the property $(XY)^T = Y^T X^T$,we get: $B^T = (

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(B) Let $B = AA^T$. To check if $B$ is symmetric,we find its transpose $B^T$. $B^T = (AA^T)^T$. Using the property $(XY)^T = Y^T X^T$,we get: $B^T = (A^T)^T A^T$. Since $(A^T)^T = A$,we have: $B^T = AA^T = B$. Since $B^T = B$,the matrix $AA^T$ is a symmetric matrix.

Class 12 Mathematics 3-4. Matrices and Determinants Special types of matrices, Transpose of matrices and Trace of matrices

Medium

For any square matrix $A$,$AA^T$ is a

A
Unit matrix
B
Symmetric matrix
C
Skew symmetric matrix
D
Diagonal matrix

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3-4. Matrices and Determinants

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Special types of matrices, Transpose of matrices and Trace of matrices

Which one of the following statements is correct regarding skew-symmetric matrices?

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Find the transpose of the following matrix: $\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$

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If the matrix $A$ is both symmetric and skew-symmetric,then

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If $A = \begin{bmatrix} 5 & 2x+3 \\ x-2 & x+1 \end{bmatrix}$ is a symmetric matrix,then $x$ is equal to:

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If $A$ and $B$ are symmetric matrices of the same order,then $AB - BA$ is . . . . . . .

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For any square matrix $A$,$AA^T$ is a

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Which one of the following statements is correct regarding skew-symmetric matrices?

Find the transpose of the following matrix: $\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$

If the matrix $A$ is both symmetric and skew-symmetric,then

If $A = \begin{bmatrix} 5 & 2x+3 \\ x-2 & x+1 \end{bmatrix}$ is a symmetric matrix,then $x$ is equal to:

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