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If there is a statement involving the natural number n such that:

1. The statement is true for $n = 1$
2. When the statement is true for $n = k ($where $k$ is some positive integer$),$ then the statement is also true for $n = k + 1.$

Then, the statement is true for all natural numbers n.
Also, if $A$ is a square matrix of order n, then $A^2$ is defined as $AA$. In general, $A^m = AA .... A (m$ times$)$. where m is any positive integer.
Based on the above information, answer the following questions.

1. If $\text{A}=\begin{bmatrix}3&-4\\1&-1\end{bmatrix},$ then for any positive integer n,

1. $\text{A}^\text{n}=\begin{bmatrix}3\text{n}&-4\text{n}\\\text{n}&-\text{n}\end{bmatrix}$
2. $\text{A}^\text{n}=\begin{bmatrix}1+2\text{n}&-4\text{n}\\\text{n}&1-2\text{n}\end{bmatrix}$
3. $\text{A}^\text{n}=\begin{bmatrix}3\text{n}&-8\text{n}\\1&-\text{n}\end{bmatrix}$
4. $\text{A}^\text{n}=\begin{bmatrix}1+3\text{n}&-4\text{n}\\\text{n}&1-3\text{n}\end{bmatrix}$

2. If $\text{A}=\begin{bmatrix}1&2\\0&1\end{bmatrix},$ then $|A^n|$, where $\text{n}\in\text{ N},$ is equal to:

1. $2^n$
2. $3^n$
3. $n$
4. $1$

3. If $\text{A}=\begin{bmatrix}1&0\\1&1\end{bmatrix}$ and $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ then which of the following holds for all natural numbers $\text{n}\geq1?$

1. $A^n= nA - (n - 1)I$
2. $A^n = 2^{n-1} A - (n - 1)I$
3. $A^n= nA + (n - 1)I$
4. $A^n = 2^{n-1} A + (n - 1)I$

4. Let $\text{A}=\begin{bmatrix}\text{a}&0&0\\0&\text{a}&0\\0&0&\text{a}\end{bmatrix}$ and $\text{A}^\text{n}=[\text{a}_{\text{ij}}]_{3\times3}$ for some positive integer n, then the cofactor of $a_{13}$ is:

1. $a^n$
2. $-a^n$
3. $2a^n$
4. $0$

5. If $A$ is a square matrix such that $|A| = 2,$ then for any positive integer n, $|A^n|$ is equal to:

1. $0$
2. $2n$
3. $2^n$
4. $n^2$