Question

A=(1/0 1/1) where nEN then A* is​

Answer 1

Answer:

$\bf\,A^n=\left(\begin{array}{cc}1&0\\n&1\end{array}\right)$

Step-by-step explanation:

$\text{Given: }$

$\boxed{\bf\,A=\left(\begin{array}{cc}1&0\\1 &1\end{array}\right)}$

$A^2=\left(\begin{array}{cc}1&0\\1 &1\end{array}\right)\times\left(\begin{array}{cc}1&0\\1 &1\end{array}\right)$

$\implies\,A^2=\left(\begin{array}{cc}1+0&0+0\\1+1&0+1\end{array}\right)$

$\implies\,\boxed{\bf\,A^2=\left(\begin{array}{cc}1&0\\2&1\end{array}\right)}$

$\text{similarly,}$

$\boxed{\bf\,A^3=\left(\begin{array}{cc}1&0\\3&1\end{array}\right)}$

$\boxed{\bf\,A^4=\left(\begin{array}{cc}1&0\\4&1\end{array}\right)}$

and so on

$\text{Hence }$

$\boxed{\bf\,A^n=\left(\begin{array}{cc}1&0\\n&1\end{array}\right)}$