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?

If A and B are two matrices such that AB is of order n × n, then which one of the following is correct?

How many matrices of different orders are possible with elements comprising all prime numbers less than 30?