Matrix Calculator – Solve Matrix Operations Online
Add, multiply and invert 2x2 matrices, with determinants.
About the Matrix Calculator (2x2)
What is the Matrix Calculator (2x2)?
A matrix calculator operates on 2×2 matrices: addition, multiplication, determinants and inversion.
Why use this calculator?
Matrix algebra powers computer graphics, machine learning and systems of equations. The 2×2 case shows every idea clearly by hand.
How to use it
- Enter the eight entries of matrices A and B.
- Pick the operation.
- Read the result matrix, determinant or inverse.
Formula
2×2 inverse: (1/det)·[[a₂₂, −a₁₂],[−a₂₁, a₁₁]].
A matrix with determinant 0 (singular) has no inverse and the calculator explains why.
Frequently Asked Questions
What does det(A) = 0 mean?
The matrix squashes area to zero — it has no inverse and its rows/columns are linearly dependent.
Why check A × A⁻¹?
The product should be the identity matrix; the check row shows it actually is.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.
How accurate are the results?
We use standard, widely accepted formulas and calculate in your browser using double-precision arithmetic. Results are rounded for readability, so treat them as reliable estimates rather than a guarantee. Real-world factors can vary the true figure.
Can I add this calculator to my own website?
Yes. Open this calculator page and use the "Add to your website" box in the sidebar to copy a ready-made iframe snippet, then paste it into any HTML page.
Does it work on a phone or tablet?
Yes. The layout is fully responsive, so it works on desktops, laptops, tablets and mobile phones, and every input adapts to touch screens.