00:00 Intro

00:50 Determinant of a matrix A

01:32 First property of determinant

03:40 Second property of determinant

04:57 Third property of determinant

06:50 Credits

Q1: Which property is not one of the determinant?

A1: $| \det(A) |$ is the volume of the parallelepiped spanned by the columns of $A$.

A2: $\det(A)$ is zero if and only if the columns of $A$ are linearly independent.

A3: $\det(\mathbf{1}) = 1$

A4: The sign of $\det(A)$ gives orientation of the vectors given by the columns of $A$.

Q2: Which statement is correct?

A1: $\det \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} = 1$

A2: $\det \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} = -1$

A3: $\det \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} = 0$

A4: One needs more information.