Last updated: August 1, 2026
Matrix Addition and Subtraction Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Enter Matrix A and Matrix B in the same row-based format and choose add or subtract. The calculator checks that both matrices have identical dimensions, combines the entries position by position, and returns the resulting matrix together with the accepted dimensions and the operation used.
Enter two matrices of the same size and choose add or subtract to combine them entry by entry.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
For equal-sized matrices, (A ± B)ij = aij ± bij.
Where:
- A=first matrix
- B=second matrix
- A ± B=entry-wise sum or difference
Worked Examples
Add two 2×2 matrices
Compute [[1,2],[3,4]] + [[5,6],[7,8]].
- 1Match entries by position.
- 2Add each pair.
- 3Keep the same shape.
Subtract two 2×2 matrices
Compute A - B for the same pair.
- 1Match entries by position.
- 2Subtract B from A entry by entry.
Decimal entries
Work with finite decimals.
- 1Enter the rows.
- 2Combine corresponding positions.
- 3Review the rounded output.
Dimension mismatch
A 2×2 and 2×3 matrix cannot be added.
- 1Compare shapes first.
- 2Stop when the dimensions differ.
Introduction
Add or subtract two matrices entry by entry when their shapes match.
Overview
Add or subtract two matrices entry by entry when their shapes match.
Result matrix
Basic matrix algebra homework
Comparing coefficient tables
Transformation updates
Input format
Use the same row-based format for both matrices.
Separate rows with semicolons
Separate entries with commas or spaces
Brackets are optional
Keep row lengths consistent
Formula and method
For equal-sized matrices, (A ± B)ij = aij ± bij.
- A matters:
first matrix.
- B matters:
second matrix.
- A ± B matters:
entry-wise sum or difference.
Validation rules
The calculator uses deterministic validation before it computes the final result.
Both matrices must be rectangular
Both matrices must have the same dimensions
The operation must be add or subtract
Every entry must be finite
Interpreting the outputs
Use the main result first, then the secondary fields to verify the structure and meaning of the answer.
The result matrix keeps the common shape
dimensions confirms the accepted size
operationUsed echoes the chosen mode
Subtraction is always A - B in that order
Common use cases
These are typical reasons to use this calculator in study or applied work.
Basic matrix algebra homework
Comparing coefficient tables
Transformation updates
Quick element-wise checks
FAQs
Why must the matrices have the same size?
Because each entry in A needs a matching entry in B.
Can I use decimals or negatives?
Yes. Any finite real entries are supported.
Does subtract mean B - A?
No. The subtract option computes A - B.
How do I enter a 3×3 matrix?
Use a format like 1,2,3;4,5,6;7,8,9.
Is this the same as matrix multiplication?
No. Addition and subtraction are entry-wise operations.
What if my rows have different lengths?
The calculator rejects the input because the matrix is not rectangular.