Statement 1: If 'A' is an invertible matrix, then (A²)⁻¹ = (A⁻¹)² Statement 2: If 'A' is an invertible matrix, then |A⁻¹| = |A|⁻¹

Answer: (c) Both the statements are true. (A²)⁻¹=(AA)⁻¹=A⁻¹A⁻¹=(A⁻¹)² and |A||A⁻¹|=|I|=1, so |A⁻¹|=|A|⁻¹. Correct: (c)

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Statement 1: If 'A' is an invertible matrix, then (A²)⁻¹ = (A⁻¹)² Statement 2: If 'A' is an…

Statement 1: If '$A$' is an invertible matrix, then $(A^2)^{-1} = (A^{-1})^2$ Statement 2: If '$A$' is an invertible matrix, then $|A^{-1}| = |A|^{-1}$

(a)Statement 1 is true and Statement 2 is false.
(b)Statement 2 is true and Statement 1 is false.
(c)Both the statements are true.
(d)Both the statements are false.

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Answer

Correct option: (c)

Answer: (c) Both the statements are true. $(A^2)^{-1}=(AA)^{-1}=A^{-1}A^{-1}=(A^{-1})^2$ and $|A||A^{-1}|=|I|=1$, so $|A^{-1}|=|A|^{-1}$.