Q.

Let A be an invertible matrix. Which of the following is not true?

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a

AT−1=A−1T

b

A−1=|A|−1

c

A−2=|A|−1

d

A−1=|A|−1

answer is B.

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Detailed Solution

We know that AT−1=A−1TSo, option (a) is true.In option  (b), A−1 is a matrix and |A|−1  is a number. So, it is not true. Now,A2A−12=(AA)A−1A−1⇒ A2A−12=AAA−1A−1=(AI)A−1=AA−1=I∴ A2−1=A−12So, option (c) is true.
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