Answer :

Given.


We need to find A2 – 5A – 14I.


We know A2 = A × A.






Now, we evaluate –5A = –5 × A.





Finally, matrix –14I = –14 × I.





The given expression is A2 – 5A – 14I.





On multiplying both sides with matrix A, we get


A (A2 – 5A – 14I) = O


A3 – 5A2 – 14(A × I) = O


A3 – 5A2 – 14A = O


A3 = 5A2 + 14A







Thus, and .


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