Question

If A= (001, 010, 100) then A^4 is equal to

1) A
2) 2A
3) I
4) 4A

Answer 1

Answer:

2) 2A is your answer

Step-by-step explanation:

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Answer 2

Given matrix  $A = \begin{bmatrix}0 & 0 & 1\\ 0 & 1 & 0\\ 1& 0& 0\end{bmatrix}$

We need to find the matrix $A^4$

What is the matrix?

A matrix is a rectangular array or table with rows and columns of numbers, symbols, or expressions that is used to represent a mathematical object or an attribute of one. is a matrix having two rows and three columns, for instance.

Now $A^4=A^2 \times A^2$

Now we find $A^2=\begin{bmatrix}0 & 0 & 1\\ 0 & 1 & 0\\ 1& 0& 0\end{bmatrix} \times \begin{bmatrix}0 & 0 & 1\\ 0 & 1 & 0\\ 1& 0& 0\end{bmatrix}$

$\Rughtarrow A^2 = \begin{bmatrix}1+0+0 & 0+0+0 & 0+0+0\\ 0+0+0 & 0+1+0 & 0+0+0\\ 0+0+1& 0+0+0& 0+0+0\end{bmatrix}$

$\therefore A^2 = \begin{bmatrix}1 & 0 & 0\\ 0 &1 & 0\\ 0& 0& 1\end{bmatrix}$

$\therefore A^2 =I$

Now, $A^4=A^2 \times A^2$

$\Rightarrow A^4=I \times I\\\Rightarrow A^4=I$

$\therefore A^4 = \begin{bmatrix}1 & 0 & 0\\ 0 &1 & 0\\ 0& 0& 1\end{bmatrix}$

Hence, the required answer is the identity matrix of $3 \times 3$ .

To learn more about matrix from the given link

https://brainly.in/question/8398908

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