2×2Identität

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 notation "2x2" indicates that the matrix has 2 rows and 2 columns.

The 2x2 identity matrix, often denoted as I or I₂, plays a crucial role in matrix operations. When multiplied with any 2x2 matrix A, the result is A:

A * I₂ = I₂ * A = A

This property is analogous to the number 1 in scalar multiplication, where any number multiplied by 1 remains unchanged. The identity matrix is fundamental for concepts such as matrix inversion, where the product of a matrix and its inverse yields the identity matrix. It also appears in various transformations in geometry and in solving systems of linear equations.