Inverse Matrices Calculator

Square matrix. Rows separated by a semicolon or newline, entries by spaces or commas.
Inverse
0.6 -0.7; -0.2 0.4
Matrix Inverse Calculator
Determinant
10
Invertible
yes
Order (n)
2
Rank
2
Adjugate matrix
6 -7; -2 4
Cofactor matrix
6 -2; -7 4
Method used
Adjugate formula: adj(A) / det(A)
Largest error in A A⁻¹ - I
0
Worked out from Gilbert Strang, Introduction to Linear Algebra, ch. 2.5 (inverse matrices) and ch. 5.3 (Cramer's rule, adjugate) and 1 other source.

How this is worked out

13 steps
  1. Matrix is 2x2.
  2. [ 4 7 ]
  3. [ 2 6 ]
  4. det(A) = 10
  5. Cofactor matrix C, where C(i,j) = (-1)^(i+j) det(minor(i,j)):
  6. [ 6 -2 ]
  7. [ -7 4 ]
  8. adj(A) = Cᵀ:
  9. [ 6 -7 ]
  10. [ -2 4 ]
  11. A⁻¹ = adj(A) / det(A) = adj(A) / 10:
  12. [ 0.6 -0.7 ]
  13. [ -0.2 0.4 ]
Inverse matrixtable
01
0.6-0.7
-0.20.4

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