NIMCET 2018 Question Paper with solutions

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Question : 44 of 120

Marks: +1, -0

If A is an invertible skew symmetric matrix, then

A^{-1}

is a

symmetric matrix
skew-symmetric matrix
zero matrix
identity matrix

Solution:

We have, A is skew-symmetric matrix.
∴

A^T

= - A
⇒

(A^T)^{-1}

=

(-A)^{-1}

⇒

(A^{-1})^T

= -

A^{-1}

∴

A^{-1}

is also skew-symmetric matrix.

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