(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 and 4 .Determinants and Matrices 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 and 4 .Determinants and Matrices

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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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If $A$ is a square matrix and $A + A^T$ is a symmetric matrix,then $A - A^T$ is:

The matrix $\begin{bmatrix} 0 & 5 & -7 \\ -5 & 0 & 11 \\ 7 & -11 & 0 \end{bmatrix}$ is known as:

If $A'$ and $B'$ are the transpose matrices of the square matrices $A$ and $B$ respectively,then $(AB)'$ is equal to:

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