https://file.aiquickdraw.com/mathbot/file/1727520001581qkgacxg1.jpg

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.

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

Find out which type of matrix has an inverse in this detailed linear algebra problem. Learn about singular, non-singular, and square matrices, and explore the key theorems and formulas used to determine invertibility.

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