Q.If $A = \begin{pmatrix} 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{pmatrix}$ , then $A^{50} + B^{50}$ equals

\begin{pmatrix} 101 & 100 & 50 \ 0 & 101 & 100 \ 0 & 0 & 101 \end{pmatrix}

\begin{pmatrix} 101 & 100 & 4950 \ 0 & 101 & 100 \ 0 & 0 & 101 \end{pmatrix}

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

\begin{pmatrix} 51 & 50 & 1225 \ 0 & 51 & 50 \ 0 & 0 & 51 \end{pmatrix}

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

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Q.If A=(111 011 001)A = \begin{pmatrix} 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{pmatrix}A=(1​1​1 0​1​1 0​0​1​) and B=(111 011 001)B = \begin{pmatrix} 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{pmatrix}B=(1​1​1 0​1​1 0​0​1​), then A50+B50A^{50} + B^{50}A50+B50 equals