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线性代数证明题A square matrix is called skew-symmetric if AT = ..A.

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线性代数证明题
A square matrix is called skew-symmetric if AT = ..A.Prove that if A
is an (2k +1)(2k +1) skew-symmetric,k = N(natural number),then A is a nonsingular
matrix.
线性代数证明题A square matrix is called skew-symmetric if AT = ..A.
skew-symmetric 反对称矩阵.应该满足 A^T = - A .
奇数阶反对称矩阵应该是奇异的(或退化的)
但题目让证明它是 非退化的.
是不是题目有误?