Work out identity matrix instantly with clear inputs, formula shown and shareable results.
The identity matrix has ones on the diagonal and zeros elsewhere, and leaves every vector unchanged. Scaling it by k gives a uniform dilation with determinant kⁿ and trace nk.
Identity
Iᵢⱼ = 1 if i = j, otherwise 0; AI = IA = A
1, and scaling it by k gives k⁴.
It is the multiplicative identity for matrices, which is what makes the notion of an inverse meaningful.