Question

If $A^2+A-I=0$, then $A^{-1}$ =

• A. $I+A$
• B. $I-A$
• C. $-I+A$
• D. $-I-A$

Answer 1

Answer: (A)

$I+A$

$A^2+A-I=0$

multiplying both sides with $A^{-1}$ gives

$A^{-1}{A}^2+A^{-1}A-A^{-1}I=0$

$\Rightarrow A+I-A^{-1}=0$

$\Rightarrow A^{-1}=I+A$

Hence, option A.