For any invertible matrix A , which of the following is NOT true.

The correct answer is Option (3) → \( (\mathrm{adj}\,A)^{-1}=|A|A \)

Each option is a statement about an invertible matrix A; the one marked Incorrect is the statement that is not true.

Option (1) \( |A|\ne0 \) — Correct. An invertible matrix has a non-zero determinant.

Option (2) \( (A')^{-1}=(A^{-1})' \) — Correct. Transposing \( AA^{-1}=I \) gives \( (A^{-1})'A'=I \).

Option (3) \( (\mathrm{adj}\,A)^{-1}=|A|A \) — Incorrect. Since \( \mathrm{adj}\,A=|A|A^{-1} \), the inverse is \( (\mathrm{adj}\,A)^{-1}=\frac{1}{|A|}A \), not \( |A|A \).

Option (4) \( |A^{-1}|=|A|^{-1} \) — Correct. \( |A|\,|A^{-1}|=|I|=1 \).