For the matrix A=find the numbers a and b such that A2 + aA + bI = O.

For the matrix A=find the numbers a and b such that A2 + aA + bI = O. 
Answer :

Plug the values in A² + aA + bI = O 

Solve it we get

                 … (1)

Equate the corresponding element we get

4+a = 0

a = - 4

and

3+a+b = 0

Plug the value of a = - 4 we get

3- 4+ b = 0

b = 1

plug the value in equation 1 we get

  

hence a = -4 and b = 1 satisfied the condition

We have A² + aA + bI = O

Plug the value of a and b

A² - 4A + I = O

Multiply by A^-1  we get

A² A^-1- 4A A^-1 + I A^-1 = O A^-1

A – 4I +A^-1 =  O

A^-1 = 4I – A

Plug the value we get