If find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = O.

OR

If find (A’)^-1.

Given that,

Now ,

Now, A² – 5A + 4I + X = O

⇒ X = -( A² – 5A + 4I)

OR

We have,

Now,

= 1(-1-8)-0(-2-6)-2(-8+3)

=-9+10 = 1≠ 0

⇒ A’ is invertible.

Co-factors are ,

Similarly we can find all co-factors

C₁₁ = -9 , C₁₂ = 8, C₁₃ = -5

C₂₁ = -8 , C₂₂ = 7, C₂₃ = -4

C₃₁ = -2 , C₃₂ = 2, C₃₃ = -1

∴