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Define symmetric & skew symmetric matrix...

Define symmetric & skew symmetric matrix and give and example to each.

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Symmetric matrix: A square matrix A is said to be symmetric if `A^(T) = A` skew symmetric matrix: A square matrix A is said to be skew symmetric if `A^(T) = - A`
Ex : `A = [(0,-1),(1,0)]`
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Knowledge Check

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

    A
    1
    B
    -1
    C
    0
    D
    None

  • The inverse of a skew symmetric matrix of odd order is

    A
    a symmetric matrix
    B
    a skew symmetric matrix
    C
    diagonal matrix
    D
    does not exist

  • A is a symmetric matrix or skew symmetric matrix. Then A^(2) is

    A
    an orthogonal matrix
    B
    a symmetric matrix
    C
    a unit matrix
    D
    a diagonal matrix

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    If A is a skew symmetric matrix and n is an even positive integer then A^(n) is

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