Define a skew-symmetric matrix.

Express the matrix [(2,3),(-7,5)] as the sum of a symmetric and a skew-symmetric and a skew-symmetric matrix.

Express the matrix A=[42-13571-21] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix A=[3-41-1] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix A=[323453245] as the sum of a symmetric and a skew-symmetric matrix.

......... Matrix is both symmetric and skew-symmetric matrix.

......... Matrix is both symmetric and skew-symmetric matrix.

If A is a skew -symmetric matrix , then show that A^(2) is a symmetric matrix .

Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.

Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.

Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.