Determinant of a singular 3×3 matrix

The determinant of the singular 3×3 matrix with rows (1, 2, 3), (4, 5, 6), (7, 8, 9) is 0. See the full step-by-step working and edit the matrix to try your own.

The 3x3 matrix with rows (1, 2, 3), (4, 5, 6), (7, 8, 9) has determinant 0. The calculator below is loaded with it, so you can follow every step or edit the entries.

Matrix A — fractions like 3/4 are fine

Why the answer is 0

Row 3 minus row 2 equals row 2 minus row 1, so the rows are dependent and the determinant vanishes.

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Frequently asked questions

What is the determinant of this singular 3×3 matrix?

It is 0. Row 3 minus row 2 equals row 2 minus row 1, so the rows are dependent and the determinant vanishes.

Why is this determinant zero?

A zero determinant means the rows are linearly dependent, so the matrix collapses space into a lower dimension and cannot be inverted.

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 singular 3×3 matrix with rows (1, 2, 3), (4, 5, 6), (7, 8, 9) is 0. See the full step-by-step working and edit the matrix to try your own.

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