CBSE Class 12 Maths Chapter 3 Important Formulas: Matrices

Types of Matrices

If you are searching for Matrix formulas for Class 12,  then it is very important that you should know the basic definitions also.

Different type of mattresses are there so some of them are:

1. Row Matrix - Row matrix is the matrix which can have any number of columns but it must have only one row.

2. Column Matrix - Column matrix is the matrix which can have any number of rows but it must have only one column.

3. Rectangular Matrix - A matrix in which the number of rows and number of columns is not equal is called a rectangular matrix.

4. Square Matrix - A matrix having the same number of rows and number of columns is called a square matrix.

5. Diagonal Matrix - A square matrix is called a diagonal Matrix if all the diagonal elements are non-zero, rest all are zero.

6. Scalar Matrix - A square Matrix in which all the elements except the diagonal elements are 0 and the diagonal elements are equal.

7. Unit Matrix - A square matrix is called a unit matrix if all the elements except the diagonal elements are 0 and the diagonal elements are one.

8. Equal Matrix - Two Matrices are said to be equal if the number of rows and columns in the first matrix is equal to the number of rows and columns of the second Matrix and the corresponding elements of both the matrices are equal.

9. Singular Matrix - A matrix is said to be a singular Matrix if the determinant of a is zero.

10. Non-Singular Matrix - A matrix is said to be a null singular Matrix and determinant of the matrix is not zero.

Algebra of Matrices

One of the most important topics in Matrices formula Class 12 is the algebra of matrices. Algebra of matrices includes the addition of matrices, subtraction of matrices,  multiplication of matrices, and multiplication of matrices by a scalar.

• Addition of Matrices

Two matrix A and  B can be added if and only if the order of matrix A is equal to the order of matrix  B.

\[A = [a_{ij}]_{m \times n}\]

\[B = [b_{ij}]_{m \times n}\]

\[A + B = [a_{ij} + b_{ij}]_{m \times n}\]

Properties of Addition of Matrices

1. Commutative Law - Addition of mattresses follow commutative law.  

A + B = B+ A

2. Associative Law - Addition of matrices follow associative law.

A + (B + C) = (A + B) + C

3. Additive Inverse - If matrix A  is the matrix then Matrix (-A ) is the additive inverse for matrix A.

A + ( -A ) = 0

4. Identity of the Matrix - For a matrix A, 0 is the additive identity of the matrix when,

A + 0 = 0 + A

5. Cancellation Properties

For matrices A, B and C,

If A + B = A + C 

Then, B = C  (This is known as left cancellation)

Similarly,

For matrices A, B and C

If B + A = C + A

Then, B = C (This is known as Right Cancellation)

• Subtraction of Matrices

Two matrices A and B can be subtracted if and only if the order of matrix A is equal to the order of matrix B.

If A is a matrix of order M x N similarly be is a matrix of order M x N then,

\[A - B = [a_{ij} - b_{ij}]_{m \times n}\]

• Multiplication of Matrices

One of the most important concepts and formulas is the multiplication of matrices from the formulas of matrices Class 12.

For two matrices A and B,  multiplication of matrices can be done if the number of rows of the first matrix is equal to the number of columns of the second matrix.

If,

\[A = [a_{ij}]_{m \times n}\]

\[B = [b_{ij}]_{m \times n}\]

\[AB = c_{ij} = \sum_{k=1}^{n} a_{ik}b_{kj}\]

Other Related Links for Class 12 Maths Chapter 3

• Matrices – Types, Operations, Properties and Examples

• NCERT Class 12 Maths Chapter 3 Solutions in English

• Class 12 Maths Revision Notes for Matrices of Chapter 3

• Important Questions for CBSE Class 12 Maths Chapter 3 - Matrices