2x2Identität

2x2Identität refers to the identity matrix of size 2x2. In linear algebra, an identity matrix is a square matrix that, when multiplied by another matrix, leaves the other matrix unchanged. For a 2x2 matrix, this is represented as:

[[1, 0],

[0, 1]]

This matrix has ones on the main diagonal from the top-left to the bottom-right and zeros everywhere else. The key property of the 2x2 identity matrix, often denoted as I or I₂, is that for any 2x2 matrix A, the following holds true:

A * I₂ = I₂ * A = A

This property makes the 2x2 identity matrix analogous to the number 1 in scalar multiplication. It plays a crucial role in matrix operations, transformations, and solving systems of linear equations. For instance, when performing matrix inversion, the identity matrix is used to check if the inverse is calculated correctly, as a matrix multiplied by its inverse yields the identity matrix. In the context of linear transformations, the 2x2 identity matrix represents the identity transformation, which maps every vector to itself without any change.