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Matrix Entrywise Product up to 3 × 3

Multiply corresponding entries of two equally sized matrices, from 1 × 1 through 3 × 3, with signed and zero entries and retained inverse relations.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For A = [[2, −3], [0, 5]] and B = [[4, 2], [7, −1]], the entrywise product is [[8, −6], [0, −5]]. Each output uses only the entries at the same row and column.

Cᵢⱼ = Aᵢⱼ × Bᵢⱼ

Worked example

Enter these known values and leave the other values blank.

A (1, 1)
2
A (1, 2)
-3
A (2, 1)
0
A (2, 2)
5
B (1, 1)
4
B (1, 2)
2
B (2, 1)
7
B (2, 2)
-1
Product (1, 1)
8
Product (1, 2)
-6
Product (2, 1)
0
Product (2, 2)
-5

Assumptions and limitations

  • Both matrices use the same selected row and column counts, each from one to three. Indices in labels are row first, column second.
  • This is the Hadamard or entrywise product. Ordinary matrix multiplication instead sums row-by-column products and is a different operation.
  • Signed and zero entries are accepted. Solving one factor from a product requires the other factor to be nonzero; a zero product with a zero known factor cannot determine the missing factor.
  • Changing dimensions hides entries outside the chosen shape and retains their values for when you expand the matrix again.

Common questions

Does order matter for this product?

For real-number entries, swapping the two matrices gives the same corresponding-entry products. This property does not generally hold for ordinary matrix multiplication.

References

Bookify corrects the second-row third-column product and its inverse variants to use b3 and y3. The source incorrectly reused b2 and y2 for that entry.

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