Properties of Determinants - Linear Algebra

In this video we will learn some properties of determinant of a matrix.

Properties of Determinants of Matrices:
Determinant evaluated across any column or row is same.
If all the elements of a row (or column) are zeros, then the value of the determinant is zero.
Determinant of a Identity matrix is 1.
If rows and columns are interchanged then value of determinant remains same (value is the same). Therefore, det(A) = det(A^T), here A^T is transpose of matrix A.
If any two row (or two column) of a determinant are interchanged the value of the determinant is multiplied by -1.
If all elements of a row (or column) of a determinant are multiplied by some scalar number k, the value of the new determinant is k times of the given determinant.
If two rows (or columns) of a determinant are identical the value of the determinant is zero.
Let A and B be two matrix, then det(AB) = det(A)*det(B).
Determinant of Inverse of matrix is equal to inverse of the original matrix

[lornabaumanwyss]

So helpful and well explained. Thank you.