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) $\left( A ^{ T }\right)^{-1}=\left( A ^{-1}\right)^{ T }$