(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 3-4. Matrices and Determinants 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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3-4. Matrices and Determinants

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

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

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