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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
a 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^–1A)' = (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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