# Inverse Matrix Calculator English Español

Matrices are array of numbers or values represented in rows and columns. Inverse of a matrix A is the reverse of it, represented as A-1. Matrices, when multiplied by its inverse will give a resultant identity matrix. 3x3 identity matrices involves 3 rows and 3 columns. In the below Inverse Matrix calculator, enter the values for Matrix (A) and click calculate and calculator will provide you the Adjoint (adj A), Determinant (|A|) and Inverse of a 3x3 Matrix.

## Inverse of a 3x3 Matrix

Matrices are array of numbers or values represented in rows and columns. Inverse of a matrix A is the reverse of it, represented as A-1. Matrices, when multiplied by its inverse will give a resultant identity matrix. 3x3 identity matrices involves 3 rows and 3 columns. In the below Inverse Matrix calculator, enter the values for Matrix (A) and click calculate and calculator will provide you the Adjoint (adj A), Determinant (|A|) and Inverse of a 3x3 Matrix.

Code to add this calci to your website  ### Example:

If the Matrix A is,

 1 2 3 4 2 1 5 4 2

Inverse Matrix is,
A-1 = 1 / det (A) [adj (A)]

Step 1 :
Cofactor of each element

#### A11 =

+
 2 1 4 2
= 4 - 4 = 0

#### A12 =

-
 4 1 5 2
= -(8 - 5) = -3

#### A13 =

+
 4 2 5 4
= 16 - 10 = 6

#### A21 =

-
 2 3 4 2
= -(4 - 12) = -8

#### A22 =

+
 1 3 5 2
= 2 - 15 = -13

#### A23 =

-
 1 2 5 4
= -(4 - 10) = 6

#### A31 =

+
 2 3 2 1
= 2 - 6 = -4

#### A32 =

-
 1 3 4 1
= -(1 - 12) = 11

#### A33 =

+
 1 2 4 2
= 2 - 8 = -6
Cofactor Matrix :
 0 -3 6 8 -13 6 -4 11 -6

Step 2 :
Adj(A) is Transpose of Cofactor Matrix :

 0 8 -4 -3 -13 11 6 6 -6

Step 3 :
A -1 = 1 / det (A) {

 0 8 -4 -3 -13 11 6 6 -6

}

Step 4 :
det (A) = [1 (4-4) ] - [2(8-5)] + [3(16-10)]
= [0 - 6 + 18] = 12

Hence, Inverse of a 3x3 Matrix is
A-1 = 1 / 12 {

 0 8 -4 -3 -13 11 6 6 -6

}