Question

if a=[ 0 1 1 0] and |a^2020| = 2k then k =​

Answer 1

Given : $A = \left[\begin{array}{cc}0&1\\1&0\end{array}\right]$   | A²⁰²⁰ | =  2k

To Find : K

Solution:

$A = \left[\begin{array}{cc}0&1\\1&0\end{array}\right]$

$A^{2} =A.A = \left[\begin{array}{cc}0&1\\1&0\end{array}\right] \left[\begin{array}{cc}0&1\\1&0\end{array}\right]$

$= \left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

A² = I

Iⁿ = I

A²⁰²⁰ = (A²)¹⁰¹⁰  = I¹⁰¹⁰  = I

A²⁰²⁰ = I

=> | A²⁰²⁰ | = | I  |

=>  | A²⁰²⁰ | = 1

2k  =  1

=> k  = 1/2

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