(A) Given that $A$ is a symmetric matrix,we have $A^T = A$.To check if $A^n$ is symmetric,we need to find the transpose of $A^n$,which is $(A^n)^T$.Us

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(A) Given that $A$ is a symmetric matrix,we have $A^T = A$.To check if $A^n$ is symmetric,we need to find the transpose of $A^n$,which is $(A^n)^T$.Using the property of transpose $(A^k)^T = (A^T)^k$,we get:$(A^n)^T = (A^T)^n$Since $A^T = A$,we substitute this into the equation:$(A^n)^T = (A)^n = A^n$Since $(A^n)^T = A^n$,it follows that $A^n$ is a symmetric matrix.

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

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If $A$ is a symmetric matrix and $n \in N$,then $A^n$ is

A
Symmetric
B
Skew symmetric
C
$A$ diagonal matrix
D
None of these

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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 symmetric matrix and $n \in N$,then $A^n$ is

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