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Select whether the matrix is 2 by 2 or 3 by 3.
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DeterminantInvertible
10

The scalar det(A). Only defined for square matrices.

Invertible?Yes
Inverse matrix A⁻¹[0.6, -0.7; -0.2, 0.4]
Transpose Aᵀ[4, 2; 7, 6]
Trace10
Adjugate (adj A)[6, -7; -2, 4]
Rank2
Determinant10
Trace10
Rank2

The determinant is 10, so this 2x2 matrix is invertible.

  • |det(A)| = 10 is the factor by which the matrix scales area.
  • A negative determinant means the transformation also flips orientation.
  • The inverse is computed by dividing the adjugate matrix by the determinant.

Next stepUse the inverse to solve the linear system A x = b as x = A inverse times b.

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