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Question

Assertion :If A is a non-singular symmetric matrix, then its inverse is also symmetric.
Because Reason: (A−1)T=(AT)−1, where A is a non-singular symmetric matrix.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let A be an invertible matrix. Than there exists a matrix B such that
AB=In=BA
|AB|=|In|
|A||B|=1(|AB|=|A||B|)
|A|0
A is non-singular matrix.
Conversely, if A is non-singular, then
A.(adjA)(A)=InA1=adjA|A|

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