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

Question:

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

A. A is a diagonal matrix

B. A is a zero matrix

C. A is a square matrix

D. None of these

Solution:

If A is both symmetric and skew-symmetric matrix, then we should have

$A^{\prime}=A$ and $A^{\prime}=-A$

$\Rightarrow A=-A$

$\Rightarrow A+A=O$

$\Rightarrow 2 A=O$

$\Rightarrow A=O$

Therefore, A is a zero matrix.