Diagonal Matrix: Overview, Questions, Preparation

A diagonal matrix is defined as a square matrix with all the other entries 0 except the principal elements. Various properties can help in determining a matrix as a diagonal matrix. These properties are:

• In addition or multiplication of the same order matrix, you get a diagonal matrix as a result.
• The transpose of every matrix is equal to the original matrix itself.
• Diagonal Matrices are commutative when they are multiplied with each other.

Other Matrices

Apart from this, there are several other matrices as well. All these matrices have different formulas, properties and ways of solving them. With every matrix, you get some different property, so it is better to learn it and memorise it. Some of the commonly used and taught matrices include symmetric matrix, skew-symmetric matrix, hermitian matrix, orthogonal matrix, idempotent matrix, nilpotent matrix, involuntary matrix, and a lot of others.

Matrices are not just a part of your 11th and 12th syllabus but also an important part of higher studies such as B.Tech and other competitive exams. If you find difficulty in learning this chapter, you can always take help, but it won’t be wise if you keep neglecting this chapter. Also, a chapter named as determinant and Matrices in 12th standard holds a lot of marks in the finals. 

Many new things are taught in the 11th standard. When it comes to mathematics, there is another chapter named as matrices. “Introduction to Matrices” is a very important chapter not just from the 11th final exam’s point of view but for competitive exams as well. It is a chapter that holds approximately 8+ marks in the final examinations and a lot of significance in the future. Various types of matrices are taught to the students in the 11th class, and one amongst them is the Diagonal Matrices.

Q: What are the two ways by which a diagonal matrix remains diagonal?

Q: What will be the transpose of a diagonal matrix?

Q: How can someone identify a diagonal matrix?

Q: Are there any other forms of matrices?

Q: What happens when two diagonal matrices are multiplied?