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If a matrix A is Symmetric as well as Skew-Symmetric, then:

  1. A is a diagonal matrix
  2. A is a unit matirx
  3. A is a triangular matirx
  4. A is a null matrix

Answer (Detailed Solution Below)

Option 4 : A is a null matrix
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Detailed Solution

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Concept:

Consider a matrix A is skew-symmetric, then AT = −A
and A is symmetric, then AT = A

Calculation:

Since, A is skew-symmetric.
AT = −A
Since, A is symmetric.
AT = A
⇒ −A = A
⇒2A = O
⇒A = O
Hence, A is a null matrix.

Hence, option (4) is correct.

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