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Give me a moment to process it.The image contains multiple-choice questions in Russian, related to matrix theory and linear algebra. Here's a breakdown of the questions:

1. Basic Minors of a Matrix (Базисным минором матрицы называется):

Options:

• Minor of order $k$, if all minors of order $k$ are equal to zero, but at least one minor of order $k+1$ is non-zero.
• Minor of order $k+1$, if all minors of order $k+1$ are zero, but at least one minor of order $k+1$ is non-zero.
• Non-zero minor of order $k+1$, if all minors of order $k+1$ are zero.
• Minor of order $k+1$, if all minors of order $k+1$ are zero, and the rank of the matrix is $k+1$.

2. Choose the Incorrect Statement (Выберите неверное утверждение):

The statements are about the conditions for a system of linear algebraic equations (СЛАУ) to have unique or infinite solutions:

• For a homogeneous square system to have a nontrivial solution, the rank of the matrix must be less than the number of variables.
• For a homogeneous square system to have a trivial solution, the determinant of the matrix must be non-zero.
• For a homogeneous square system to have a trivial solution, the rank of the matrix must equal the number of variables.
• If a homogeneous system has a nontrivial solution, at least one variable is free.

3. Specify All Correct Statements (Укажите все верные утверждения):

This section includes statements about matrices, determinants, and inverse matrices:

• For a matrix to have an inverse, the determinant must not be zero.
• If $A$ and $B$ are inverse matrices, then $AB = BA = I$.
• If the determinant of a matrix is not zero, then $A^{-1} = \frac{1}{\det(A)} \text{adj}(A)$.
• If $A$ and $B$ are inverse matrices, the transpose of $B$ is also an inverse of $A$.

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