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Determinants of 2×2 and 3×3 Matrices

The determinant is a single number squeezed out of a square matrix, and it answers a surprisingly large question: whether the matrix can be inverted at all.

This quiz covers the 2×2 formula, expansion for 3×3, the shortcut for triangular matrices, and the properties worth knowing — what a zero row does, what swapping rows does, and what happens when every entry is scaled.

Plenty of calculation here, so keep something to write on nearby.

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What This Quiz Covers

  • The 2×2 determinant formula
  • Expanding a 3×3 determinant
  • Triangular matrices as a shortcut
  • What a determinant of zero means
  • Row swaps and scaling
  • The determinant of a product and of a transpose
Sample questions3 of 13 shown
Q1
For which matrices is a determinant defined?
Q2
What is the determinant of [[3, 5], [2, 4]]?
Q3
What is the determinant of [[6, 3], [4, 2]]?
Answer all 13 questions on Cletica →

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