Identity Matrix
The matrix I with 1s on the diagonal; AI = A.
Key idea
The matrix I with 1s on the diagonal; AI = A.
In depth
The identity I has ones on the diagonal and zeros elsewhere, with AI = IA = A. It represents the transformation that leaves everything unchanged, like the number 1.
Worked example
For 2 × 2: I = [1 0; 0 1]. A · I = A.
Formula
Real-world uses
- Starting point for solving equations by row reduction and for leaving data unchanged in code
Common mistake
Using an identity of the wrong size.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Identity Matrix?
The matrix I with 1s on the diagonal; AI = A. It is a topic at the advanced level in Linear Algebra.
What is the formula for Identity Matrix?
The key formula is AI = IA = A.
Where is Identity Matrix used in real life?
Real-world examples: Starting point for solving equations by row reduction and for leaving data unchanged in code.
What should I learn before Identity Matrix?
Make sure you are comfortable with Matrix Multiplication, the previous topic in Linear Algebra.
What is a common mistake with Identity Matrix?
Using an identity of the wrong size.
How can I practise Identity Matrix?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Identity Matrix?
Move on to Transpose next.
Related advanced topics in Linear Algebra
- Dot Product – Sum of component products.
- Angle Between Vectors – Cosine from the dot product.
- Orthogonality – Vectors are orthogonal when their dot product is 0.
- Projection – Component of one vector along another.
- Cross Product – A vector perpendicular to two vectors in 3D.
- Lines and Planes in Vector Form – Parametric and normal equations.