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

Options

A. `(A^T)^(-1)=(A^(-1))^T`
B. `A^(-1)=abs(A)^(-1)`
C. `(A^2)^(-1)=(A^(-1))^2`
D. `abs(A^(-1))=abs(A)^(-1)`

Answer

B

Explanation

We know that `(A^T)^(-1)=(A^(-1))^t`
So, option (a) is true.
In option (b) `A^(-1)` is matrix and `abs(A)^(-1)`is a number .
So, it is not true.
Now,
`A^2(A^(-1))^2=(A A)(A^(-1)A^(-1))`
`rArr A^2(A^(-1))^2=A(A A^(-1))A^(-1)=(AI)A^(-1)=A A^(-1)=I`
`:. (A^2)^(-1)=(A^(-1))^2`
So, option (c) is true.