A matrix is a rectangular grid of numbers.
About this calculator
A matrix is a rectangular grid of numbers. You use them in linear algebra, computer graphics, statistics, and engineering systems. This calculator handles the operations most students need without installing software.
Type matrix A as comma-separated values with semicolons between rows. Example: 1, 2; 3, 4 is a 2×2 matrix. For add, subtract, or multiply, enter matrix B in the same format. Transpose, determinant, and inverse use matrix A only.
Addition and subtraction need matching dimensions. Multiplication needs the column count of A to equal the row count of B. The 2×2 inverse exists only when the determinant is not zero.
For equation systems try the [[linear-equation]] calculator. For larger numeric work pair this with the [[scientific-notation]] calculator when entries are very large or small.
Common uses
- Add or subtract matrices for linear algebra homework
- Multiply transformation matrices in 2D graphics problems
- Find 2×2 or 3×3 determinants for Cramer
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Frequently asked questions
How do I enter a matrix in this calculator?
Separate values in a row with commas and separate rows with semicolons. 1, 0, 2; 3, 4, 5 is a 2×3 matrix with first row 1, 0, 2 and second row 3, 4, 5.
When can I multiply two matrices?
A (m×n) can multiply B (n×p) only when the inner dimensions match — columns of A equal rows of B. The result is m×p.
What is the determinant of a 2×2 matrix?
For [[a, b], [c, d]], det = ad − bc. Example: [[1, 2], [3, 4]] gives 1×4 − 2×3 = −2. Zero determinant means no inverse exists.
Why does inverse fail for some 2×2 matrices?
A matrix has no inverse when its determinant is zero — the rows are linearly dependent. Example: [[1, 2], [2, 4]] has det 0 because row 2 is twice row 1.