Let A= 12 34 1 -12 , then the value of sum of all the elements of A^100 is

Correct answer: 2. A^2= 12 34 1 -12 12 34 1 -12 = 1 0 0 1 ⇒A^2=Ι⇒A^100=Ι⇒sum=2

Q24 / 75 · NTA Abhyas (JEE Main) 2020 · Mathematics · Matrices

Let $A = [\begin{matrix} \frac{1}{2} & \frac{3}{4} \\ 1 & \frac{- 1}{2} \end{matrix}]$ , then the value of sum of all the elements of $A^{100}$ is

Correct answer: 2

A^{2} = [\begin{matrix} \frac{1}{2} & \frac{3}{4} \\ 1 & \frac{- 1}{2} \end{matrix}] [\begin{matrix} \frac{1}{2} & \frac{3}{4} \\ 1 & \frac{- 1}{2} \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

\Rightarrow A^{2} = Ι \Rightarrow A^{100} = Ι \Rightarrow s u m = 2

Hence, the correct answer is 2.