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### Course: Algebra (all content)>Unit 20

Lesson 15: Determinants & inverses of large matrices

# Inverting a 3x3 matrix using determinants Part 2: Adjugate matrix

Sal shows how to find the inverse of a 3x3 matrix using its determinant. In Part 2 we complete the process by finding the determinant of the matrix and its adjugate matrix. Created by Sal Khan.

## Want to join the conversation?

• At , what is meaning of det(c)?
• det(c) is the abbreviation for "the determinant of c."
• What if you got a non regular matrix ( det(c)=0 )). Then you can use this example ?
• A matrix has no inverse if its determinant is zero.
• If matrices were defined by humans, why on earth would we design such a convoluted way to find the inverse of a matrix? What problems does this complicated process solve?
• If you could provide a less convoluted solution, then I think that you might have the Field's medal coming your way in the future :-)
• What if the determinant is 0? Wouldn't that make everything in the inverse matrix undefined?
• Yes. The inverse is undefined.(since we don't know how to divide by 0)
• Why is the adjugate (transpose) for a 2x2 matrix different from that of a 3x3? Wikipedia shows the 3x3 method shown here as applicable for a 2x2 as well.

http://en.wikipedia.org/wiki/Transpose

Look at how Sal writes the adjugate for a 2x2 in the link below.

• An adjugate matrix is the transpose of the cofactor matrix, not of the original square matrix.
• Is there a general method of inverting n*n matrix?
• As far as I understood this methode can be used as a general method of inverting an n*n matrix. (But of course the technique sal used to get the determinant can't be used for n*n matrices, so you would have to find another technique there.)
• : Wouldn't it be easier to say TRANSPOSE instead of ADJUGATE?! At least would be better to say that T is something that is more used when it comes to studying matrices more? (Í know its the same thing but might confuce students like me who are having exam about this and never heard of adjugate and instead of TRANSPOSE T)
• Adjugate of matrix A is "Transpose of Cofactor matrix of A"