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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 A² 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 |Aⁿ|, where $\text{n}\in\text{ N},$ is equal to:
   

1. 2ⁿ
2. 3ⁿ
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. Aⁿ = nA - (n - 1)I
2. Aⁿ = 2^n-1 A - (n - 1)I
3. Aⁿ = nA + (n - 1)I
4. Aⁿ = 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 a₁₃ is:
   

1. aⁿ
2. -aⁿ
3. 2aⁿ
4. 0

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

1. 0
2. 2n
3. 2ⁿ
4. n²