Enter matrices using numbers, fractions, or radicals. Multiply them instantly and inspect each derived entry. Save outputs as CSV or PDF for later review.
| Item | Sample Data |
|---|---|
| Matrix A | [ [sqrt(4), 1], [3, sqrt(9)] ] |
| Matrix B | [ [1, sqrt(16)], [2, 5] ] |
| Product Matrix | [ [4, 13], [9, 27] ] |
| Square Root Matrix | [ [2, 3.6056], [3, 5.1962] ] |
Matrix multiplication follows a row-by-column rule. If Matrix A has size m × n and Matrix B has size n × p, then the product Matrix C has size m × p.
Each result entry is calculated with this formula:
C[i][j] = Σ (A[i][k] × B[k][j])
The calculator also supports square root expressions inside cells, such as sqrt(16). After multiplication, it can optionally compute the element-wise square root of every result entry. Real square roots exist only for non-negative values.
Matrix multiplication is a core operation in mathematics. It appears in algebra, statistics, graphics, engineering, and data science. This calculator helps you multiply two matrices quickly. It also accepts square root expressions inside each matrix cell. That saves time when your values are written as radicals.
The most common mistake in matrix multiplication is a dimension mismatch. The first matrix columns must equal the second matrix rows. This page checks that rule before computing anything. That helps learners understand the structure of matrix products. It also reduces input errors during homework and exam practice.
You can enter values like 4, 3/2, or sqrt(25). The calculator evaluates each cell and then multiplies the matrices using the row-by-column formula. Every result entry is computed from paired products and sums. This makes the tool useful for clean classroom examples and more advanced numerical work.
The output section shows the product matrix first. It can also display the element-wise square root of the product when real roots exist. In addition, the page reports row sums, column sums, trace, and Frobenius norm. These details help you verify patterns inside the matrix and review the scale of the result.
The example data table shows a sample setup with radical entries. The formula section explains the multiplication rule in simple terms. The how-to section gives step-by-step guidance. Export buttons let you save your calculated output as CSV or PDF. That makes the page practical for study notes, worksheets, and quick reports.
The page uses a simple layout with minimal styling. The result appears above the form after submission. That keeps the answer easy to review. The calculator area uses a responsive grid, so it remains readable across screen sizes. It is a direct tool for matrix multiplication with square root support and clear output.
You can enter matrices from 1 × 1 up to 6 × 6. The key rule is that Matrix A columns must equal Matrix B rows.
Yes. You can enter values like sqrt(4), sqrt(49), or combinations such as 3 + sqrt(9). The calculator evaluates them before multiplication.
Yes. Entries like 1/2, 3/4, and 7/3 are accepted. They are converted into decimal values during the calculation process.
It computes the element-wise square root of the product matrix. Negative entries are marked as not real because real square roots do not exist for them.
The trace is the sum of the main diagonal entries. It is available only when the product matrix is square.
It is the square root of the sum of all squared entries in the product matrix. It gives a single measure of matrix magnitude.
That error appears when Matrix A columns do not match Matrix B rows. Matrix multiplication is undefined in that case.
Yes. Use the CSV button to download table data and the PDF button to save a formatted summary of the current result.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.