Determinant of a 2×2 rotation-style matrix
The determinant of the 2×2 rotation-style matrix with rows (0, -1), (1, 0) is 1. See the full step-by-step working and edit the matrix to try your own.
The 2x2 matrix with rows (0, -1), (1, 0) has determinant 1. The calculator below is loaded with it, so you can follow every step or edit the entries.
Why the answer is 1
Rotations preserve area, so their determinant is 1.
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Frequently asked questions
What is the determinant of this 2×2 rotation-style matrix? ▾
It is 1. Rotations preserve area, so their determinant is 1.
Is this matrix invertible? ▾
Yes. The determinant is 1, which is not zero, so the matrix has an inverse and its rows are linearly independent.
Can I change the numbers? ▾
Yes — the calculator above is fully editable. Type over any entry and the determinant and every step recalculate immediately.
About this Calculator
The determinant of the 2×2 rotation-style matrix with rows (0, -1), (1, 0) is 1. See the full step-by-step working and edit the matrix to try your own.