If the matrix A is both symmetric and skew symmetric, then - Vidyadip

Question

If the matrix A is both symmetric and skew symmetric, then

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Answer

Only a null matrix can be symmetric as well as skew symmetric.
In Symmetric Matrix $A^T= A,$
Skew Symmetric Matrix $A^T= -A,$
Given that the matrix is satisfying both the properties.
Therefore, Equating the RHS we get $A = -A$ i.e, $2A = 0.$
Therefore $A = 0,$ which is a null matrix.

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