Method
Matrix products use row-by-column dot products. For A=[[a,b],[c,d]], det(A)=ad−bc and A⁻¹=(1/det)[[d,−b],[−c,a]].
Math worksheet
2×2 Matrix Calculator
Add, subtract or multiply two 2×2 matrices, or inspect the determinant and inverse of matrix A with a full cell audit.
The calculation runs locally. Exact-integer tools avoid floating point; decimal and transcendental tools report rounding limits.
Method and verification guide
How the 2×2 Matrix Calculator works
Matrix products use row-by-column dot products. For A=[[a,b],[c,d]], det(A)=ad−bc and A⁻¹=(1/det)[[d,−b],[−c,a]]. The calculator keeps the intermediate values visible so you can reproduce the answer independently.
Interpret the result
Matrix multiplication is order-sensitive; A×B generally differs from B×A.
Check the assumptions
This focused page handles 2×2 matrices in double precision; a zero determinant means no inverse exists.
Local calculation
Everything runs in this browser. Inputs are not sent to an external calculator.
Rounding
Displayed values may be rounded for readability while calculations use full floating-point precision unless the tool explicitly uses exact integers.
Scope
This focused page handles 2×2 matrices in double precision; a zero determinant means no inverse exists.
Simple by design
Three steps to a clearer number.
Enter your details
Use realistic values in each field. You can change them anytime.
Calculate instantly
The formula runs locally, so there is no account or waiting time.
Use the result
Treat the answer as a practical estimate for your next decision.