Question

Let $A$ be an invertible matrix then which of the following is/are true:

• A. $\left|A^{-1}\right|=|A{|}^{-1}$
• B. ${\left(A^2\right)}^{-1}={\left(A^{-1}\right)}^2$
• C. ${\left(A^T\right)}^{-1}={\left(A^{-1}\right)}^T$
• D. none of these

Answer 1

Answer: (A), (B), (C)

Correct answer is (a) $\left|A^{-1}\right|=|A{|}^{-1}$ Correct answer is (b) ${\left(A^2\right)}^{-1}={\left(A^{-1}\right)}^2$ Correct answer is (c) ${\left(A^T\right)}^{-1}={\left(A^{-1}\right)}^T$