Determinants Matrices Question 56

Question: If A is a square matrix such that $ A^{2}=I $ where I is the identity matrix, then what is $ {A^{-1}} $ equal to-

Options:

A) $ A+1 $

B) Null matrix

C) A

D) Transpose of A

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] Let $ A^{2}=I $
    $ \Rightarrow A^{2}{A^{-1}}=I{A^{-1}} $
    $ \Rightarrow A={A^{-1}} $