Inverse Matrix Calculator
Find the inverse of a square matrix. Get instant step-by-step solutions — completely free, no signup required.
Free Inverse Matrix Calculator Calculator
Enter your problem below to get an instant step-by-step solution.
About Inverse Matrix Calculator
Find the inverse of a square matrix. Linear algebra and matrix operations are foundational to computer graphics, machine learning, and solving systems of equations. Understanding matrix manipulations is critical for advanced mathematics.
Our Inverse Matrix Calculator calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any inverse matrix calculator expression and receive a complete, verified solution with every step shown.
Inverse Matrix Calculator Formula
A⁻¹ = (1 / det A) · [[d, −b], [−c, a]] for A = [[a, b], [c, d]]
The inverse of a square matrix A is the matrix A⁻¹ with A·A⁻¹ = I. It exists only when det A ≠ 0. For a 2×2 matrix swap the diagonal, negate the off-diagonal and divide by the determinant; for larger matrices row-reduce [A | I] to [I | A⁻¹].
Worked Example
Find the inverse of A = [[4, 7], [2, 6]]
- det A = 4·6 − 7·2 = 10
- Swap and negate: [[6, −7], [−2, 4]]
- Divide by 10: [[0.6, −0.7], [−0.2, 0.4]]
- Check: A·A⁻¹ = I ✓
Answer: A⁻¹ = [[0.6, −0.7], [−0.2, 0.4]]
Common Mistakes to Avoid
- Trying to invert a matrix whose determinant is zero.
- Negating the diagonal instead of the off-diagonal entries.
- Assuming (AB)⁻¹ = A⁻¹B⁻¹ — it is B⁻¹A⁻¹.
How to Use the Inverse Matrix Calculator Calculator
- 1
Input your matrix or vector values for the Inverse Matrix Calculator problem
- 2
Press Enter or click the Solve button to run the calculation
- 3
Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Inverse Matrix Calculator formula?
A⁻¹ = (1 / det A) · [[d, −b], [−c, a]] for A = [[a, b], [c, d]]. The inverse of a square matrix A is the matrix A⁻¹ with A·A⁻¹ = I. It exists only when det A ≠ 0. For a 2×2 matrix swap the diagonal, negate the off-diagonal and divide by the determinant; for larger matrices row-reduce [A | I] to [I | A⁻¹].
Can you show a worked Inverse Matrix Calculator example?
Find the inverse of A = [[4, 7], [2, 6]]: det A = 4·6 − 7·2 = 10; Swap and negate: [[6, −7], [−2, 4]]; Divide by 10: [[0.6, −0.7], [−0.2, 0.4]]; Check: A·A⁻¹ = I ✓. Answer: A⁻¹ = [[0.6, −0.7], [−0.2, 0.4]].
Is this Inverse Matrix Calculator calculator free to use?
Yes — the Inverse Matrix Calculator calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Inverse Matrix Calculator homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.