Let A=⎡⎢⎣100101010⎤⎥⎦ satisfies An=An−2+A2−I for n≥3. And trace of a square matrix X is equal to the sum of elements in its principal diagonal. Further consider a matrix ∪3×3 with its column as ∪1,∪2,∪3 such that A50 ∪1=⎡⎢⎣12525⎤⎥⎦,A50 ∪2=⎡⎢⎣010⎤⎥⎦, A50 ∪3=⎡⎢⎣001⎤⎥⎦ Then, The value of |∪| equals

Let A=⎡⎢⎣100101010⎤⎥⎦ satisfies An=An−2+A2−I for n≥3

1.	Let A=⎡⎢⎣100101010⎤⎥⎦ satisfies An=An−2+A2−I for n≥3. And trace of a square matrix X is equal to the sum of elements in its principal diagonal. Further consider a matrix ∪3×3 with its column as ∪1,∪2,∪3 such that A50 ∪1=⎡⎢⎣12525⎤⎥⎦,A50 ∪2=⎡⎢⎣010⎤⎥⎦, A50 ∪3=⎡⎢⎣001⎤⎥⎦ Then, The value of \|∪\| equals
Answer» Let $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 1 & 0 & 1 0 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$ satisfies $A^{n} = A^{n - 2} + A^{2} - I$ for $n \geq 3.$ And trace of a square matrix $X$ is equal to the sum of elements in its principal diagonal. Further consider a matrix $\cup_{3 \times 3}$ with its column as $\cup_{1}, \cup_{2}, \cup_{3}$ such that $A^{50} \cup_{1} = ⎡ ⎢ ⎣ \begin{matrix} 12525 \end{matrix} ⎤ ⎥ ⎦, A^{50} \cup_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦, A^{50} \cup_{3} = ⎡ ⎢ ⎣ \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦$ Then, The value of $\| \cup \|$ equals