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Maths-

General

Easy

Question

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

a symmetric matrix
a skew symmetric matrix
diagonal matrix
None of these

The correct answer is: a skew symmetric matrix

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

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