Question 1
If $\mathbf{A}$ is a square matrix, what is the relationship between its determinant and its invertibility?
Question 2
For a $2 \times 2$ matrix $\mathbf{A} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, what is its inverse $\mathbf{A}^{-1}$?
Question 3
If $\mathbf{A}$ is a matrix and $\mathbf{I}$ is the identity matrix of the same order, what is the result of $\mathbf{A}\mathbf{I}$?
Question 4
Which of the following describes a transformation that involves a reflection?
Question 5
What is the definition of an eigenvalue $\lambda$ for a square matrix $\mathbf{A}$ and a non-zero vector $\mathbf{v}$?
