Matrices
Identity matrix
A square matrix with 1s on the diagonal and 0s elsewhere; it leaves a matrix unchanged when multiplied.
| English | Identity matrix |
|---|---|
| Bahasa Melayu | Matriks identiti |
| 中文 | 单位矩阵 |
How it is used
The 2×2 identity is I = (1 0; 0 1). For A = (5 2; 1 3), AI = (5 2; 1 3) = A, and IA = A too, so multiplying by I leaves A unchanged.
Where it shows up in SPM
In the Matrices chapter (Form 5), it defines what an inverse must produce: AA⁻¹ = I. Paper 1 may ask you to state or recognise the identity matrix, or to complete AA⁻¹ = I.
Don't confuse it with
Frequently asked questions
Is the identity matrix like the number 1?
Yes, in a useful way. Just as multiplying any number by 1 leaves it unchanged, multiplying any matrix by the identity leaves it unchanged: AI = IA = A.
That is why I plays the role of 1 in matrix arithmetic.
Does the identity matrix always look the same?
Its pattern is always 1s on the main diagonal and 0s everywhere else, but its size matches the matrix. At SPM level you almost always use the 2×2 identity (1 0; 0 1), since the work is with 2×2 matrices.