Let A be an invertible matrix. Which of the following is not true?
AT−1=A−1T
A−1=|A|−1
A−2=|A|−1
We know that AT−1=A−1T
So, 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−12
So, option (c) is true.