MCQ
જો $A=\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}$ તો $A^{100}=...........$
- ✓$2^{99} A$
- B$2^{101} A$
- C$2^{100} A$
- D$I$
$A^2=A.A=\begin{bmatrix}1\ & 1\\1&1\end{bmatrix}\begin{bmatrix}1& 1\\1& 1\end {bmatrix}=\begin{bmatrix}2& 2\\ 2&2\end{bmatrix}=2\begin{bmatrix}1& 1 \\1 & 1\end {bmatrix}$
$A^3=A^2.A=2\begin{bmatrix}1&1\\1&1\end{bmatrix}\begin{bmatrix} 1&1\\1&1 \end {bmatrix}$
$=4\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}$
તેવી જ રીતે
$A^{100}=2^{99}\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}=2^{99}A$
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