Generate an identity matrix of any given size. An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros.
Matrix Config
Generated Identity Matrix
3×3Matrix
Dimension
1
0
0
0
1
0
0
0
1
Determinant1
Trace3
About this calculator
What is an Identity Matrix?
An identity matrix, often denoted by I or I_n, is a square matrix of size n × n where the elements on the main diagonal (from top-left to bottom-right) are all 1, and all other elements are 0.
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Pro Tips
Multiplicative Identity: A · I = A and I · A = A.
Self-Inverse: Any identity matrix is its own inverse (I^{-1} = I).
Determinant: The determinant of any identity matrix is always 1.
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Fun Facts
"The trace (sum of diagonal elements) of an n × n identity matrix is always n."
"Identity matrices are the 'number 1' of the matrix world."
"They are essential for defining inverse matrices."
Formula: e_{ij} = δ_{ij} = { 1 if i = j, 0 if i ≠ j }
