Matrix Calculator

How it works

Perform addition, subtraction, and multiplication on 2x2 and 3x3 matrices.

Perform 2x2 and 3x3 matrix arithmetic

Description

The Matrix Calculator is a visual tool for linear algebra. It allows you to define two matrices (A and B) and perform fundamental arithmetic operations between them. With support for both 2x2 and 3x3 dimensions, it is an ideal companion for students and engineers working on systems of equations or geometric transformations.

Inputs

• Size Selection: Switch between 2x2 or 3x3 matrix formats.
• Matrix A & B: Interactive grids where you can input individual cell values.
• Operations:
  • + (Addition)
  • - (Subtraction)
  • × (Multiplication)

Outputs

• Result Matrix: A visual grid displaying the calculated values resulting from the operation.

Chart

• N/A: This tool features an interactive 2D data grid.

“Good to Know”

• Matrix Multiplication: Unlike regular numbers, matrix multiplication is not commutative ($A \times B$ is usually not the same as $B \times A$). It involves multiplying rows by columns.
• Identity Matrix: Multiplying any matrix by the Identity matrix (1s on the diagonal, 0s elsewhere) will result in the original matrix.
• Subtraction: Subtracting Matrix B from Matrix A is equivalent to $A + (-1 \times B)$.

Examples

Example 1: Simple 2x2 Addition

• Input:
  • A: [[1, 2], [3, 4]]
  • B: [[5, 6], [7, 8]]
  • Op: +
• Output: [[6, 8], [10, 12]]

Example 2: 2x2 Multiplication

• Input:
  • A: [[1, 2], [3, 4]]
  • B: [[2, 0], [1, 2]]
  • Op: ×
• Output: [[4, 4], [10, 8]]

Example 3: 3x3 Identity Check

• Input:
  • A: any 3x3 matrix
  • B: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
  • Op: ×
• Output: Exactly the same as Matrix A.