First slide

Applications of determinant

Question

If A³= O, then I+A+A²equals

Moderate

A

I-A
B

(I+A^-1)
C

(I-A)^-1
D

None of these

Solution

Given A³ = O
Nom
$\begin{matrix} (I - A) (I + A + A^{2}) = I^{2} + IA + {IA}^{2} - AI - A^{2} - A^{3} \\ = I - A 3 \\ = I \end{matrix}$
$\Rightarrow (I - A)^{- 1} = I + A + A^{2}$

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