Question

Verify Cayley Hamilton Theoremand find A inverse of matrixA =[1 2 3 ] [2 4 5] [2 5 6]​

Answer 1

Answer:

Charaacteritic equation is

|A−λI|=0⇒[2−λ312−λ]=0

⇒(2−λ)2−3=0

⇒λ2−4λ+1=0

therefore Cayley-hamiltion theorem,

A2−4A+I=OorI=4A−A2

Multiplying byA−1, we get

A−1=4A−1A−A−1AA

=4I−IA=4I−A

=4[1001]−{2312]

[2−3−12]