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Q.If $A = \begin{pmatrix} 1 & 2 & 3 \ 0 & 1 & 4 \ 0 & 0 & 1 \end{pmatrix}$ , then $A^{100}$ equals

a

\begin{pmatrix} 1 & 200 & 100 \times 199 \ 0 & 1 & 100 \ 0 & 0 & 1 \end{pmatrix}

b

\begin{pmatrix} 1 & 200 & 19800 \ 0 & 1 & 100 \ 0 & 0 & 1 \end{pmatrix}

c

\begin{pmatrix} 1 & 100 & 4950 \ 0 & 1 & 100 \ 0 & 0 & 1 \end{pmatrix}

d

\begin{pmatrix} 1 & 100 & 100 \times 99/2 \ 0 & 1 & 100 \ 0 & 0 & 1 \end{pmatrix}

Correct Answer: Option B

The correct solution involves applying the fundamental concept to derive the final value step by step...

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