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Question
If the matrix A is both symmetric and skew symmetric, then ______.
Options
A is a diagonal matrix
A is a zero matrix
A is a square matrix
None of these
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Solution
If the matrix A is both symmetric and skew symmetric, then A is a zero matrix.
Explanation:
Consider the matrix A.
Clearly A' = A and A' = –A
∴ A = –A
⇒ 2A = 0
⇒ A = 0
∴ A is a zero matrix.
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