Matrix calculator allows you to find the matrix addition, subtraction, multiplication, transpose, inverse, and determinant online.
Using this online matrix calculator, you can easily find the solution for your matrix problems. It supports almost all the operations. You can add, subtract, or multiply matrices, find their inverse, calculate determinants, and so on. In short, you can say it is a onestop destination for all the operations. Also, it combines all the different calculators like matrix multiplication calculator, inverse matrix calculator, determinant calculator, and much more.
A matrix can be simply defined as a set of numbers that are arranged in rows and columns to form a rectangular array. To form a matrix, there should be at least one column or row. Also, there are different kinds of matrix and they are widely used in mathematical calculations, statistical implementations, physics, economics, computer science, and economics.
The dimensions of a matrix tell about the number of rows and columns of the matrix. It is denoted as m x n, where m is the number of rows and n is the number of columns.
Let's consider a 2 × 3 matrix A. So, it can be represented as A_{2 x 3}. It includes 2 rows and 3 columns.
The elements of the matrix can be represented in an array form as follows:
A= 

Each element in the above matrices represented as:
This is the way to represent a matrix as individual entities. The first subscript denotes row and the second one denotes column. Using this value, you can determine the position of an element easily.
The matrix calculator gives so many features in it using which you can easily find solutions to your problems.
You can easily use our matrix calculator to perform all the matrixrelated operations and the basic steps for all of them remain the same. Just follow the instructions below.
This is the main context that we are going to talk about in this article. Matrix operations are the set of operations that we can apply to find some results. The matrix calculator makes your task easy and fast. Also, you can perform these operations with just a few keystrokes. The most common matrix operations are addition, subtraction, multiplication, power, transpose, inverse, and calculating determinant. Let's learn all of them one by one.
Matrix addition is only performed if both matrices are the same size. In other words, the matrices to be added should have the exact same number of rows and columns. This means they should have the same dimensions.
Addition Process: When the size/dimensions of the matrices are the same then to find the sum, you need to add the corresponding elements of the matrices.
Here, A and B are the elements of the matrices to be added and C is the resultant matrix.
A = 
 B = 

C = 

C = 

Matrix subtraction is very much similar to addition. It is also performed if both matrices are the same size. In other words, both matrices should have exact same number of rows and columns.
Subtraction Process: You need to subtract the corresponding elements of the matrices.
Let's understand it from a simple example.
A = 
 B = 

C = 

C = 

There are two types of matrix multiplication we can perform.
In scalar multiplication, each element of the single matrix is multiplied by a scalar value. Let's take an example to understand it.
A = 
 B = 3 
3 × 
 = 

To multiply two matrices, the number of columns of the first matrix should be equal to the number of rows of the second matrix.
For example, you can multiply 3 × 4 with 4 × 2. But you can not multiply 3 × 4 with 2 × 4.
Note: Matrix multiplication is not a commutative property. It means, it is not necessary that A × B will always be equal to B × A.
Multiplication Process: Two matrices are multiplied by finding the dot product between the corresponding elements of the row of the first matrix and the column of the second matrix.
Here, A and B are the elements of the matrices to be multiplied and c is the resultant matrix.
A = 
 B = 

C = 

C = 

Power of matrix meaning is to raise a matrix to a given power.
For example, the given matrix is A. Now calculate matrix A with the power of 2 means: A^{2} = A × A.
Most importantly, the power can be raised to only square matrices. Because a nonsquare matrix can not be multiplied by itself.
A^{2} = 
 ^{2} 
= 

= 

The transpose of a matrix flips its elements over its diagonal. The row elements become column elements whereas the column elements become row elements. Most importantly, the matrix should not be empty.
Transpose Process: To transpose a matrix just switch the rows and column elements. If the matrix contains 2 rows and 3 columns the matrix will now consist of 3 rows and 2 columns.
Here, T is a matrix containing m rows and n columns that will become n rows and m columns after transpose.
A = 
 A^{T} = 

B = 
 B^{T} = 

The Laplace formula is widely used to calculate the determinant of the matrix of any size. Let's understand the process through this formula and example:
A= 

= 

= a(eifh)  b(difg) + c(dheg)
A= 

= 

= 3(1×4  5×3) – 5(7×4 – 5×3) + 2(7×3 – 3×1)
= 3(11) – 5(13) + 2(18)
= 62
Prerequisites: The matrix should not be empty and you should know the determinant of that matrix. Also, the determinant should not be equal to zero.
Process: To find the inverse of the matrix we use a simple formula where the inverse of the determinant is multiplied with the adjoint of the matrix.
Formula: A^{1} = ( 1 / A ) × adj(A)
Where, the adjoint of a matrix is the collection of its cofactors which are the determinants of the minor matrices.