Properties of matrices....(1)

Algebra Level 4

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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