(D) matrix $M$ is symmetric if $M' = M$.For option $A$: $(A + A')' = A' + (A')' = A' + A = A + A'$. Thus,$A + A'$ is symmetric.For option $B$: $(AA')'

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(D) matrix $M$ is symmetric if $M' = M$.For option $A$: $(A + A')' = A' + (A')' = A' + A = A + A'$. Thus,$A + A'$ is symmetric.For option $B$: $(AA')' = (A')'A' = AA'$. Thus,$AA'$ is symmetric.For option $C$: $(A'A)' = A'(A')' = A'A$. Thus,$A'A$ is symmetric.For option $D$: $(A - A')' = A' - (A')' = A' - A = -(A - A')$. Since $(A - A')' = -(A - A')$,the matrix $A - A'$ is skew-symmetric,not symmetric.

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

Easy

If $A$ is a square matrix,then which of the following matrices is not symmetric?

A
$A + A'$
B
$AA'$
C
$A'A$
D
$A - A'$

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Class 12

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3 and 4 .Determinants and Matrices

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

Find the transpose of the following matrix: $\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right]$.

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If $A$ is a symmetric matrix,then the matrix $M'AM$ is

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If $A = \begin{bmatrix} 1 & -2 \\ 5 & 3 \end{bmatrix}$,then $A + A^T$ equals:

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Express the matrix $B=\left[\begin{array}{rrr}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]$ as the sum of a symmetric and a skew symmetric matrix.

Medium

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If for the matrix $A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix}$,$AA^{T} = I_{2}$,then the value of $\alpha^{4} + \beta^{4}$ is ....... .

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If $A$ is a square matrix,then which of the following matrices is not symmetric?

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Find the transpose of the following matrix: $\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right]$.

If $A$ is a symmetric matrix,then the matrix $M'AM$ is

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