# 3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy | Summary and Q&A

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November 2, 2009
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Khan Academy
3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy

## TL;DR

Determinants are used to determine if a matrix has an inverse and can be computed using specific formulas.

## Questions & Answers

### Q: What is the determinant of a 2x2 matrix?

The determinant of a 2x2 matrix is computed using the formula ad - bc.

### Q: How is the determinant related to finding the inverse of a matrix?

The determinant of a matrix is used to determine if the matrix has an inverse. If the determinant is not zero, the matrix is invertible.

### Q: How is the determinant of a 3x3 matrix computed?

The determinant of a 3x3 matrix is computed by expanding along the first row and recursively finding the determinant of the resulting 2x2 submatrices.

### Q: What does the determinant of a 3x3 matrix indicate?

The determinant of a 3x3 matrix determines if the matrix is invertible. If the determinant is not zero, the matrix is invertible.

## Summary & Key Takeaways

• An explanation of the determinant of a 2x2 matrix and its formula: ad - bc.

• The determinant of a 2x2 matrix determines if the matrix is invertible.

• Introduction to the determinant of a 3x3 matrix and its computation.

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