Perform operations on 2×2 and 3×3 matrices — addition, subtraction, multiplication, determinant, transpose, and inverse.
A Matrix Calculator performs mathematical operations on matrices, which are rectangular arrays of numbers arranged in rows and columns, fundamental to linear algebra and used in graphics, engineering, and machine learning.
Addition and subtraction combine corresponding elements of two matrices. Multiplication follows row by column rules. Determinant gives a scalar value showing key matrix properties. Transpose flips rows into columns.
Select the matrix size, such as 2x2 or 3x3. Enter the numerical values for each cell. Choose the operation you want. Click Calculate to see the result instantly.
Example 1 Addition: Matrix A is 1,2,3,4 and Matrix B is 5,6,7,8, so A plus B equals 6,8,10,12.
Example 2 Determinant: For matrix 2,3,1,4 the determinant equals 2 times 4 minus 3 times 1, which is 5.
Example 3 Multiplication: Multiplying two 2x2 matrices combines rows and columns following standard rules.
Solving systems of linear equations in engineering. Computer graphics transformations like rotation and scaling. Students verifying linear algebra homework. Machine learning model calculations.
What sizes does this tool support. Most calculators support 2x2 and 3x3, covering common use cases.
What does a zero determinant mean. It means the matrix is singular and has no inverse.
Can I multiply any two matrices. No, the columns of the first must equal the rows of the second.
What is a transpose. It flips the matrix so rows become columns and columns become rows.
Why are matrices important. They power technologies like image processing and search engine ranking.