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If A is skew-symmetric matrix then A^(2)...

If A is skew-symmetric matrix then `A^(2)` is a symmetric matrix.

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To prove that if \( A \) is a skew-symmetric matrix, then \( A^2 \) is a symmetric matrix, we can follow these steps: ### Step 1: Definition of Skew-Symmetric Matrix A matrix \( A \) is called skew-symmetric if \( A^T = -A \). This means that the transpose of \( A \) is equal to the negative of \( A \). ### Step 2: Find the Transpose of \( A^2 \) We need to find the transpose of \( A^2 \): \[ ...
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Knowledge Check

  • If A is skew-symmetric matrix, then trace of A is

    A
    1
    B
    `-1`
    C
    0
    D
    none of these

  • If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

    A
    `[{:(-4,-2),(-1,4):}]`
    B
    `[{:(4,-2),(-1,-4):}]`
    C
    `[{:(4,-2),(1,-4):}]`
    D
    `[{:(-4,2),(1,4):}]`

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