Suppose 𝐴 is an 𝑛 × 𝑛 invertible matrix. Which of the following statements is FALSE?单项选择题

A

𝐴 x = b has a unique solution for all vectors b in 𝑅 𝑛 .

B

For any 𝑛 × 𝑛 matrix 𝐵 , we have 𝐴 2 𝐵 𝐴 − 1 = 𝐴 𝐵 .

C

𝐴 ⊤ 𝐴 is an invertible matrix.

D

𝐴 − 1 = ( 𝐴 ⊤ 𝐴 ) − 1 𝐴 ⊤

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