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DETERMINANTS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDETERMINANTS2 Marks
Question
Let $A$ be a square matrix such that $A^2 - A + I = 0,$ then write $A^{-1}$ interms of $A.$
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Answer

$A^2 - A + I = 0$
$Px-$multiplying with $A^{-1},$
$(A^{-1} A) - (A^{-1} A) + A^{-1}I = 0$
$IA - I + A^{-1} = 0$
$A^{-1} = I - A$
Hence, $A^{-1} = I - A$

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