$\rm A=\begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$ where a ∈ ℕ, then is A¹⁰⁰ - A⁵⁰ - 2A²⁵ equal to?

where I is the identity matrix.

The inverse of a matrix A is given by $\rm \begin{bmatrix} -2 & 1 \\ \frac{3}{2} & -\frac{1}{2} \end{bmatrix}$ What is A equal to?

Let $A = \begin{bmatrix} 0 & 2 \\ -2 & 0 \end{bmatrix}$ and (mI + nA)² = A where m, n are positive real numbers and I is the identify matrix. What is (m + n) equal to?

Consider the following in respect of the matrix $\rm A = \begin{bmatrix} 1 & 1 & 1\\ 1 & 1 & 1\\ 1 & 1 & 1 \end{bmatrix}$

1. Inverse of A does not exist

2. A³ = A

3. 3A = A²

Which of the above are correct?