Matrix Calculator
The determinant of a 2 × 2 matrix is ad − bc: [[4, 7], [2, 6]] has determinant 10, so it has an inverse.
A 2 × 2 or 3 × 3 matrix.
10
- Trace
- 10
- Invertible
- yes
- Transpose
- [4, 2] [7, 6]
| col 1 | col 2 | |
|---|---|---|
| row 1 | 3/5 | -7/10 |
| row 2 | -1/5 | 2/5 |
Step-by-step solution
- det = ad − bc = 4×6 − 7×2 = 10
- A⁻¹ = (1/det) × adj(A)
Matrix Formula
det [[a, b], [c, d]] = ad − bc
A⁻¹ = (1/det) adj(A); no inverse when det = 0
Worked Example
The matrix [[4, 7], [2, 6]]:
- det = ad − bc = 4×6 − 7×2 = 10
- A⁻¹ = (1/det) × adj(A)
Invertible: yes · Transpose: [4, 2] [7, 6]
| col 1 | col 2 | |
|---|---|---|
| row 1 | 3/5 | -7/10 |
| row 2 | -1/5 | 2/5 |
Test-day tip
Matrix questions on the ACT are usually about dimensions or a single entry of a product. Multiply row by column only for the entry asked.
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Frequently asked questions
How do I invert a 2 × 2 matrix?
Swap a and d, negate b and c, and divide every entry by ad − bc.
When can two matrices be multiplied?
When the first has as many columns as the second has rows; an m × n times an n × p matrix gives an m × p matrix.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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Scientific Converters. (2026, October 15). Matrix Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/matrix-calculator/
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Scientific Converters, "Matrix Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/matrix-calculator/