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Symmetric & Skew Symmetric Matrix
General
Grade 12

Question:

Which one of the following is wrong?
The elements on the main diagonal of a symmetric matrix are all zero
The elements on the main diagonal of a skew - symmetric matrix are all zero
For any square matrix $A, \frac{1}{2}(A + A')$ is symmetric matrix
For any square matrix $A, \frac{1}{2}(A - A')$ is skew - symmetric matrix

Step-by-Step Solution

Key Concept: General
The elements of main diagonal of skew symmetric matrix are all zero but not necessarily for symmetric matrix. $\Rightarrow \frac{A + A'}{2}$ is symmetric matrix. $\Rightarrow \frac{A - A'}{2}$ is skew symmetric matrix.
Correct Answer: A

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