Question

If a square matrix satisfies the relation $A^2+A-I=0$ then $A^{-1}$:

• A. exists and equals I + A
• B. exists and equals I - A
• C. exists and equals $A^2$
• D. none of these

Answer 1

Answer: (A)

Given, $A^2+A-I=0$
Pre Multiply it with $A^{-1}$, we get
$A+I-A^{-1}=0$
$\Rightarrow A^{-1}=I+A$
Hence, $A^{-1}$ exists and equals I + A.