Inverse Matrix Calculator
English

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

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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

}

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