Show that the elements along the main diagonal of a skew symmetric matrix are all zero.

Pls. answer

For a skew symmetric matrix A

A^{T} + A = 0

Therefore

A^{T} = -A---------eq.1

We know

Diagonal elements of A = Diagonal elements of A^{T} ------eq.2

Now from eq.1 and eq.2

Diaganol elements of A and Diagonal elements of AT should be equal as well as of opposite signs

This is possible only when all diagonal elements are 0

Hence Proved.

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