Matrix Calculator: Operations & Inverse

Matrix calculator: add, subtract, multiply, inverse, and determinant

Bridge operations into Result C, unary ops on A/B, live determinant and trace, Logic Trace for each c_ij. Sizes 1×1–10×10; runs locally.

What this calculator does

The widget edits matrices A and B (1×1 through 10×10) and writes bridge results to Result matrix C: addition, subtraction, multiplication, scalar multiply (C = x·A or C = x·B), and copy (C = B). Unary controls on each panel transpose, raise a square matrix to a power (n = 0–6), or replace it with its inverse when det ≠ 0. Square matrices show |A|, |B|, and traces in Properties as you edit. Logic Trace explains every entry of C for bridge ops only.

Size rules:

± requires matching m×n on A and B; × requires cols(A) = rows(B).

How the math works

Addition and subtraction are element-wise on matching indices. Scalar multiply scales every entry. For AB with A of size m×n and B of size n×p, each c_i,j is the dot product of row i of A and column j of B.

c_{i,j}=\sum_{k=1}^{n} a_{i,k}\,b_{k,j}

Secondary dot-product check (not a form default): row [1, 2, 3] with column [4, 5, 6] gives 1×4 + 2×5 + 3×6 = 32. Transpose swaps indices. Inverse exists when det A ≠ 0 for square A. Power multiplies A by itself n times (n up to 6 on the form).

Limits

Maximum 10×10 per matrix. Cell display uses three decimal places; very small magnitudes use scientific notation in Result C. Logic Trace accordion kicks in beyond 20 lines. No symbolic simplification, eigenvalues, or complex matrix functions. Determinant uses Laplace expansion in code; large integers may show floating-point noise in Properties.

Matrix Calculator FAQ

What does the default layout show?

Both matrices start as 2×2 with + selected on the bridge. With default zeros, Result C is all 0.000. Use Fill → All 1 on A and B to see each c_i,j = 2.000 and four Logic Trace lines (c₁₁ through c₂₂).

When are + and − enabled vs ×?

+ and − require the same rows and columns on A and B (buttons disable when sizes differ). × requires cols(A) = rows(B); with × selected and a mismatch, Result C shows an amber dimension note. Product size follows

(m\times n)(n\times p)\to m\times p

(e.g. 2×3 times 3×2 → 2×2).

Where do determinant, trace, and inverse appear?

For square A or B, |A|, tr(A), and the same for B update live in each panel’s Properties row (shows No data while every cell is zero). Inv replaces the selected matrix with its inverse when det ≠ 0; singular matrices show Matrix is singular (determinant = 0). No inverse. Result C is not used for Inv or Det.

What bridge ops write Result matrix C?

+, −, ×, C = x·A, C = x·B, and C = B (copy B into C). Scalars default to 1 in the × boxes under each matrix. Swap exchanges A and B in place; it is separate from C = B.

How does Logic Trace work?

Expand Show step-by-step explanation under Result C. Each row lists c_i,j with the numeric formula (+, −, dot product, or scalar). Hover a cell in C to highlight the contributing row of A and column of B (× mode). Traces longer than 20 lines group by result row.

What unary controls apply to A or B directly?

Transpose swaps rows and columns and resizes the panel. Power (n = 0–6, default 2) multiplies a square matrix by itself n times; n = 0 returns the identity. Det is a reminder only; the numeric determinant stays in Properties.

How are cell values rounded and displayed?

Inputs round to 3 decimal places on blur. Result C uses three decimals; values with |v| < 0.001 show in scientific notation (e.g. 1.00e-4). Logic Trace can also show reduced fractions for rational entries.

What is not supported?

Sizes above 10×10, symbolic algebra, eigenvalues, and non-numeric entries. Fractions in cells are decimal only; use the fraction calculator for rational arithmetic separately.

Matrix Calculator: Add, Subtract, Multiply, Inverse & Determinant

Matrix A

Matrix B

How to use this calculator

Reading your matrix result

Example: Default 2×2 addition after Fill → All 1

Example: 2×3 · 3×2 multiplication