No links please 122 (i) For the matrix A=122212221, show that A2-4A-5I3=0 and hence find A-1 - Maths - Matrices

Question

No links please 122
( i )   F o r   t h e   m a t r i x   A = 1 2 2
2 1 2 2 2 1 ,   s h o w   t h a t   A 2 - 4 A - 5 I
3 = 0   a n d   h e n c e   f i n d   A - 1

Md.Ashraf Khan · Accepted Answer

No links please 122 ( i ) F o r t h e m a t r i x A = 1 2 2 2 1 2 2 2 1 , s h o w t h a t A 2 - 4 A - 5 I 3 = 0 a n d h e n c e f i n d A - 1

No links please 122
$(i) F o r t h e m a t r i x A = (\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix}), s h o w t h a t A^{2} - 4 A - 5 I_{3} = 0 a n d h e n c e f i n d A^{- 1}$