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Question

A matrix which is both symmetric as well as skew-symmetric is a null matrix. Prove.


Solution

Step 1: If a matrix is both symmetric and skew symmetric matrix ,then
A is symmetric matrix
⇒aij=aji
A is a skew symmetric matrix
⇒aij=−aji
Step 2: If aij=aji=−aji
⇒aij=0⇒aij=0
Hence A is a zero or null matrix.

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