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  4. A is a square matrix and Ι is an identity matrix of the same order. If A3=O, then inverse of matrix (Ι - A) is

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Q. $A$ is a square matrix and $Ι$ is an identity matrix of the same order. If $A^{3}=O,$ then inverse of matrix $\left(Ι - A\right)$ is

NTA AbhyasNTA Abhyas 2020Matrices

Solution:

We know,
$\left(I - A\right)\left(Ι + A + A^{2}\right)=Ι-A^{3}=Ι$
Hence, $\left(Ι - A\right)^{- 1}=Ι+A+A^{2}$