Use exp(x) for eˣ and mod(a,b) for the remainder. Roots and logarithms may return complex values.
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How to use the matrix calculator
Choose addition, subtraction, multiplication, determinant, inverse or transpose.
Enter one matrix row per line, separating values with spaces or commas. Fraction entries such as 1/2 are accepted.
For an operation using two matrices, enter Matrix B and check the dimensions.
Select Calculate. Use Copy to copy the result; matrix cells are separated by tabs.
Formula and method
(AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ; det([[a,b],[c,d]]) = ad − bc
When matrix dimensions are compatible
Addition and subtraction require the same number of rows and columns. For A × B, the number of columns in A must equal the number of rows in B. The product has the row count of A and the column count of B. Matrix multiplication generally depends on order: AB need not equal BA.
Determinant, inverse and transpose
A determinant is defined here for a square matrix. An inverse exists only for a nonsingular square matrix. For a 2 × 2 matrix, divide [[d,−b],[−c,a]] by ad−bc. A transpose swaps rows with columns and does not require a square matrix.
Solve a quadratic, including complex roots, or a system of two or three simultaneous linear equations. Degenerate quadratic inputs are handled as linear equations.
Evaluate a real-valued function over a range of x values. Choose start, end and step; each table supports up to 201 rows.
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Matrix Calculator worked examples
Multiply two 2 × 2 matrices
A=[[1,2],[3,4]], B=[[5,6],[7,8]]
[[19,22],[43,50]]
The first cell is 1×5+2×7=19. Repeat each row-by-column dot product for the other cells.
Invert a nonsingular matrix
A=[[1,2],[3,4]]
[[-2,1],[1.5,-0.5]]
The determinant is 1×4−2×3=−2. Dividing [[4,−2],[−3,1]] by −2 gives the inverse.
READ THE RESULT WITH CONTEXT
Accuracy, notation and limits
Enter rectangular matrices containing real numeric values, with at most four rows and four columns. Complex matrix entries and symbolic variables are not supported. Fraction inputs are evaluated numerically; matrix output is not an exact rational proof.
Ill-conditioned matrices can amplify rounding errors. For an inverse, check that A × A⁻¹ is approximately the identity matrix rather than relying only on a displayed determinant.
Yes, provided the column count of A equals the row count of B and both matrices meet the 4 × 4 size limit.
Why does an inverse return an error?
The input must be square and nonsingular. A zero determinant means no inverse exists. A numerically unstable matrix may also fail or produce an inaccurate inverse.
How do I enter matrix rows?
Start a new line for each row. Enter spaces or commas between values and keep the same number of entries in every row.
Calculation library: math.js. This page is an independent CalcPebble tool.