6. Vectors and Matrices

Determinants Inverse — Quiz

Test your understanding of determinants inverse with 5 practice questions.

Practice Questions

Question 1

Given a matrix $A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$, what is the determinant of its inverse, $ \det(A^{-1}) $?

Question 2

If $A$ is an invertible matrix and $k$ is a non-zero scalar, which of the following is true about the determinant of $kA$?

Question 3

Consider the matrix $A = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{pmatrix}$. What is the determinant of $A$?

Question 4

Given the matrix $A = \begin{pmatrix} 1 & x \\ 2 & 4 \end{pmatrix}$, for what value of $x$ will the matrix be singular (non-invertible)?

Question 5

If $A$ is an invertible matrix of order $3 \times 3$ and $ \det(A) = 5 $, what is the determinant of the adjoint of $A$, denoted as $ \det(\text{adj}(A)) $?