If find A2 – 5A + 4I and hence find a matrix X such that A2 – 5A + 4I + X = O.
Given.
We need to find A2 – 5A + 4I.
We know A2 = A × A.
Now, we evaluate –5A = –5 × A.
Finally, matrix 4I = 4 × I.
The given expression is A2 – 5A + 4I.
Given that A2 – 5A + 4I + X = O
⇒ X = – (A2 – 5A + 4I)
Thus, and