Question

If $A=\left[\begin{array}{ccc}3&-4\\1&-1\end{array}\right]$ then prove that $A^{n} =\left[\begin{array}{ccc}1+2n&-4n\\n&1-2n\end{array}\right]$ where n is any positive integer.

Answer 1

Answer:

if we put

n=1.2.3.4.5... in A raise to power n

then we can get the same answer as A