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  4. If A is non-singular matrix and (A + I)(A - I) = 0 then A + A-1 = .........

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Q. If $A$ is non-singular matrix and $(A + I)(A - I) = 0$ then $A + A^{-1} =$ .........

MHT CETMHT CET 2019

Solution:

We have, $A$ is non-singular matrix
$\therefore \,\,\,\,|A|=0$
and $\,\,\,\,\, (A+I)(A-I)=0$
$\Rightarrow \,\,\,\,A^{2}-I^{2}=0$
$\Rightarrow \,\,\,\,A^{2}=I^{2}=1$
$\Rightarrow \,\,\,\,A .A=I \Rightarrow A^{-1}=A$
$\therefore \,\,\,\, A+A^{-1}=A+A=2 A$