A is a skew-symmetric matrix and n is a positive integer, then An isa)a symmetric matrixb)a skew-symmetric matrixc)a diagonal matrixd)none of theseCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Skew-Symmetric Matrix

A skew-symmetric matrix is a square matrix where the elements below the diagonal are the negatives of those above the diagonal.

Properties of Skew-Symmetric Matrix

- The diagonal elements are all zero.
- The transpose of a skew-symmetric matrix is its negative.
- The determinant of a skew-symmetric matrix is zero if the size of the matrix is odd.

An to the power of n

When we raise a matrix to the power of n, we multiply the matrix n times by itself.

An is a matrix obtained by multiplying the matrix A n times by itself.

Answer

If A is a skew-symmetric matrix and n is a positive integer, then An is not necessarily a symmetric or skew-symmetric matrix, nor is it necessarily a diagonal matrix. Therefore, the correct answer is option 'D' - none of these.

Answer

For any constant n , n(A)=A(n)and It is skew symmetric matrix if A is skew symmetricthe correct answer is B

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