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Question

The inverse of a skew symmetric matrix (if it exists) is -

  1. a symmetric matrix    
  2. a skew symmetric matrix    
  3. a diagonal matrix    
  4. None of these    

The correct answer is: a skew symmetric matrix


    We have A'= –A
    Now AA–1 = A–1 A = In
    rightwards double arrow (AA–1)' = (A–1A)' = (In)'
    rightwards double arrow(A–1)' A' = A' (A–1)' = In
    rightwards double arrow(A–1)' (–A) = (–A) (A–1)' = In
    Thus, (A–1)' = – (A–1) [inverse of a matrix is unique]

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