Let the associated matrix be denoted by A. So we have that, A=[7−11−1]
∣A−λI∣=∣∣7−λ−11−1−λ∣∣=(7−λ)(−1−λ)−1(−1)
= λ2−6λ−6
So we have that the characteristics polynomial is λ2−6λ−6 . But Cayley Hamilton's theorem states that every square matrix satisfies it characteristics equation. So we check whether A2−6A−6I=0
A2=[48−660]−6A=[−426−66]−6I=[−600−6]
So we have that A2−6A−6I=[0000]
as desired. So we have that A is invertible and hence T is invertible.
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