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

We know that $(A^T)^{-1} = (A^{-1})^T$

So, option (1) is true.

In option (2), $A^{-1}$ is a matrix and $|A|^{-1}$ is a number.

So, it is not true.

Now,

$A^2 (A^{-1})^2=(AA) (A^{-1} A^{-1})$

$⇒A^2 (A^{-1})^2=A (AA^{-1}) A^{-1} = (AI) A^{-1}=AA^{-1} = I$

$∴(A^2)^{-1}=(A^{-1})^2$

So, option (3) is true.