Let S=-1a0b;a,b∈1,2,3,…100 and let Tn=A∈S:Ann+1=I. Then the number of elements in ∩n=1100Tn is _____.

Question

Let

S = \{(\begin{matrix} - 1 & a \\ 0 & b \end{matrix}); a, b \in \{1, 2, 3, \dots 100\}\}

and let

T_{n} = \{A \in S : A^{n (n + 1)} = I\}

. Then the number of elements in

\cap_{n = 1}^{100} T_{n}

is _____.

Correct Answer

100

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