1. Inverse of a Matrix Multiplicative Inverse of a Matrix For a square matrix A, the inverse is written A -1. When A is multiplied by A -1 the result is the identity matrix I. Non-square matrices do not have inverses. AA -1 = A -1 A = I

2. Are C and D inverses?

3. Requirements to have an Inverse 1.The matrix must be square (same number of rows and columns). 2. The determinant of the matrix must not be zero

5. Evaluate the following determinant: Multiply the diagonals, and subtract:

6. The computations for 3×3 determinants are messier than for 2×2's. Various methods can be used, but the simplest is probably the following: Take a matrix A : Write down its determinant:

7. Extend the determinant's grid by rewriting the first two columns of numbers Then multiply along the down-diagonals of 3 numbers:

8. ...and along the up-diagonals of three numbers

9. Add the down-diagonals and subtract the up-diagonals:

10. Then det( A )= 1. And simplify

11. Find the determinant of the following matrix: First convert from the matrix to its determinant, with the extra columns:

12. Then multiply down and up the diagonals:

13. Then add the down-diagonals, subtract the up-diagonals, and simplify for the final answer: