- #1
mathmathmad
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Homework Statement
let I_n be as an identity matrix where a_ij = 1 when i=j
I just want to ask that is it true that all identity matrix has an inverse (determinant is not 0) for n>=2?
An Identity Matrix, also known as a Unit Matrix, is a square matrix with 1s along the main diagonal and 0s in all other positions. It is denoted as I. For example, a 3x3 Identity Matrix would look like this:
I = [1 0 0; 0 1 0; 0 0 1]
The Identity Matrix has several important properties, including being the multiplicative identity for matrices and being its own inverse. It is also used in linear algebra to solve systems of equations, and is a fundamental concept in many other mathematical and scientific fields.
For an Identity Matrix of any size, the inverse is always equal to itself. This is because when multiplied by its inverse, the resulting matrix is equal to the original Identity Matrix. In other words, I x I = I.
The notation n>=2 refers to the size of the Identity Matrix, specifically that it is a square matrix with a dimension of 2 or greater. This is important because only square matrices have an inverse, and the inverse of an Identity Matrix is only equal to itself when it is a square matrix.
No, there are no exceptions to the Inverse always being true for an Identity Matrix. As long as the Identity Matrix is a square matrix, the inverse will always be equal to itself.