Operations On Matrix | Transpose of a Matrix and Inverse of Matrix
There are 3 main operations on the matrix
- Addition of matrices:
- Subtraction of Matrices:
- Multiplication of Matrices:
- Transpose of the matrix:
- Negative of a matrix:
- Inverse of Matrix:
- Frequently Asked Question-FAQs
Addition of matrices:
Two matrices A and B can be added if they have the same orders and their corresponding entries are added.
Subtraction of Matrices:
Two matrices A and B can be subtracted if they have the same orders and their corresponding entries are subtracted.
Multiplication of Matrices:
Matrix multiplication or multiplication of matrices is one of the operations that can be performed on matrices in linear algebra.
If A and B are two given matrices then the multiplication of these matrices is possible, if A and B are compatible.
Matrix multiplication is a binary operation, that gives a matrix from two given matrices.
A and B matrices are said to be compatible if the number of columns of the A matrix is equal to the number of rows of matrix B.
Transpose of the matrix:
The transpose of a matrix is obtained by changing the rows into columns and columns into rows. Transpose of a matrix is denoted by At.
For example, if we have a matrix A
In this matrix, there are 3 rows and 3 columns. The rows will convert into columns and columns into rows.
Negative of a matrix:
If we have a matrix A,
Negative of A is obtained by changing the sign of each entry of A. The negative of A is denoted by –A.
Inverse of Matrix:
If we have a matrix A, the inverse of the matrix will be,
The inverse of the matrix is denoted by A-1.
Frequently Asked Question-FAQs
What are the basic operations in matrices?
The three most common matrix operations are addition, subtraction, and multiplication of matrices.
what is Transpose of Matrix?
The transpose of a matrix is a new matrix that is formed by exchanging the rows and columns of the original matrix.
Is matrix addition commutative?
Yes. Matrix addition is commutative
Is matrix multiplication commutative?
No. Matrix multiplication is not commutative.
Is matrix addition associative?
Yes. Matrix addition is associative.
What is the product of a matrix with a null matrix?
A matrix that has been multiplied by a null matrix will always result in a null matrix.