Determinant of Identity Matrix
An identity matrix is a square matrix in which all the elements of the main diagonal are ones, and all other elements are zeros. For example, a 3×3 identity matrix looks like this:
[Tex]I =\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right)[/Tex]
The determinant of an identity matrix of any size is always 1. This property can be understood intuitively by considering that the identity matrix represents a transformation that leaves vectors unchanged when multiplied by it. Since the determinant measures how a matrix scales the space, the determinant of an identity matrix, which doesn’t scale the space at all, is 1.
Mathematically, we can express this as:
det (I) = 1
Determinant of a Matrix with Solved Examples
Determinant of a Matrix is defined as the function that gives the unique output (real number) for every input value of the matrix. Determinant of the matrix is considered the scaling factor that is used for the transformation of a matrix. It is useful for finding the solution of a system of linear equations, the inverse of the square matrix, and others. The determinant of only square matrices exists.
Table of Content
- Determinant of Matrix Calculator
- Definition of Determinant of Matrix
- Determinant of a 1×1 Matrix
- Determinant of 2×2 Matrix
- Determinant of a 3×3 Matrix
- Determinant of 4×4 Matrix
- Determinant of Identity Matrix
- Determinant of Symmetric Matrix
- Determinant of Skew-Symmetric Matrix
- Determinant of Inverse Matrix
- Determinant of Orthogonal Matrix
- Physical Significance of Determinant
- Laplace Formula for Determinant
- Properties of Determinants of Matrix