medium difficulty9 min

Types of Matrices

Matrices are classified by shape and entry pattern, such as row matrix, column matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, zero matrix, and equal matrices.

In one line: Identity is the special scalar matrix with scalar 1.

Practice This Concept

Understand it

A row matrix has one row; a column matrix has one column.
A square matrix has equal rows and columns.
A diagonal matrix is square with all non-diagonal entries zero.
A scalar matrix is a diagonal matrix whose diagonal entries are equal.
An identity matrix has all diagonal entries 1 and all non-diagonal entries 0.
A zero matrix has every entry 0.
Two matrices are equal only when they have the same order and corresponding entries equal.

Example

[[4, 0], [0, 4]] is a scalar matrix. [[1, 0], [0, 1]] is an identity matrix of order 2. [[0, 0], [0, 0]] is a zero matrix.

Formula and rule

Identity matrix I_n: a_ij = 1 when i = j and a_ij = 0 when i ≠ j.

Scalar matrix: A = kI_n.

Equal matrices: same order and a_ij = b_ij for every corresponding position.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Classify A = [[0, 0, 0], [0, 0, 0]].

1It has 2 rows and 3 columns, so it is rectangular.
2Since every entry is 0, it is a zero matrix.
3It is not a diagonal matrix because diagonal classification in this syllabus is for square matrices.

Method you can reuse

1Find the order.
2Check whether it is square.
3Check zeros outside the main diagonal.
4Check whether diagonal entries are equal.
5Check whether diagonal entries are all 1 if identity is claimed.
6For equality, compare order first, then entries.

Visual tip

No separate diagram is needed. Classification is best shown through small 2 × 2 or 3 × 3 matrix forms.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Is [[3, 0, 0], [0, 3, 0], [0, 0, 3]] diagonal, scalar, or identity?

Think first, then show answer

It is diagonal and scalar, but not identity because the diagonal entries are 3, not 1.

Common wrong answer

Calling [[2, 0], [0, 5]] a scalar matrix; it is diagonal but not scalar because diagonal entries are unequal.

Don't mix this up

A common error is calling any matrix with zeros outside the diagonal an identity matrix. It is identity only when every diagonal entry is 1.

Exam tip

For classification questions, first check whether the matrix is square. Diagonal, scalar, and identity matrices must be square.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Asked as naming the type of a given matrix, selecting all correct classifications, or forming equations from equality of matrices.

1
Enough for 1 mark
Matrices are classified by shape and entry pattern, such as row matrix, column matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, zero matrix, and equal matrices.
2
Add for 2 marks
Example: [[4, 0], [0, 4]] is a scalar matrix. [[1, 0], [0, 1]] is an identity matrix of order 2. [[0, 0], [0, 0]] is a zero matrix.
3
Add for 3 marks
A row matrix has one row; a column matrix has one column.

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