The question in the image asks:

"Какая матрица имеет обратную?"
("Which matrix has an inverse?")

The options are:

1. квадратная невырожденная (non-singular square)
2. квадратная (square)
3. ступенчатая (triangular)
4. вырожденная (singular)

The correct answer is 1. квадратная невырожденная ("non-singular square").
A non-singular square matrix has an inverse, as it has a non-zero determinant. A singular matrix (option 4) does not have an inverse because its determinant is zero. Simply being square (option 2) doesn't guarantee invertibility, and a triangular matrix (option 3) is not necessarily invertible either unless it's also non-singular.

Would you like further details on matrix inverses or any other topic? Here are five related questions to expand on this:

1. What is the determinant of a matrix and how does it relate to invertibility?
2. How can we determine if a matrix is singular or non-singular?
3. What is the process to find the inverse of a non-singular square matrix?
4. What are triangular matrices and how do they differ from other matrix types?
5. Can a non-square matrix ever have an inverse?

Tip: A matrix is invertible if and only if its determinant is non-zero and it is square.