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Maths-

General

Easy

Question

For the matrix A = $open square brackets table row 1 1 0 row 1 2 1 row 2 1 0 end table close square brackets$ , which of the following is correct

A³+ 3A²– I = O
A³– 3A²– I = O
A³+ 2A²– I = O
A³– A²+ I = O

The correct answer is: A³– 3A²– I = O

We are given matrix A and we need to find the correct equation
$A squared equals space open square brackets table row 1 1 0 row 1 2 1 row 2 1 0 end table close square brackets space open square brackets table row 1 1 0 row 1 2 1 row 2 1 0 end table close square brackets space equals space open square brackets table row 2 3 1 row 5 6 2 row 3 4 1 end table close square brackets A squared. A space equals A cubed space equals open square brackets table row 7 9 3 row 15 19 6 row 9 12 4 end table close square brackets A cubed space minus 3 A squared space minus space I space equals 0 space space c a n space b e space v e r i f i e d space f r o m space t h e space a b o v e space m a t r i c e s$

Therefore the correct option is choice 2

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