A square non-singular matrix A satisfies $A^2-A+2I=0$, then $A^{-1} =$
Answer & explanation
Correct answer: option 2
We have,
$A^2-A +2I=0$
$⇒A-A^2 = 2I$
$⇒ A (I-A) = 2I ⇒ A\left\{\frac{1}{2}(I-A)\right\}=I ⇒ A^{-1} =\frac{1}{2}(I-A)$
A square non-singular matrix A satisfies $A^2-A+2I=0$, then $A^{-1} =$
Correct answer: option 2
We have,
$A^2-A +2I=0$
$⇒A-A^2 = 2I$
$⇒ A (I-A) = 2I ⇒ A\left\{\frac{1}{2}(I-A)\right\}=I ⇒ A^{-1} =\frac{1}{2}(I-A)$