# Properties of matrices....(1)

Algebra Level 3

Consider a skew symetric matrix A of order m×m (m is a natural number) then if m=2k+1 for some natural number k then which of the following statements are true:-

$$\mathbf{1.}$$ Trace of A is zero

$$\mathbf{2.}$$ Determinant of A is zero

$$\mathbf{3.}$$ Inverse of A does not exist

$$\mathbf{4.}$$ Transpose of A is equal to additive inverse of A

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