# Worksheet: Inverse of a 3x3 Matrix

In this worksheet, we will practice finding the inverse matrix for a given three-by-three matrix.

**Q1: **

By considering the value of the determinant, determine whether the matrix has an inverse. If so, find the inverse by considering the matrix of cofactors.

- AIt has an inverse, .
- BIt has an inverse, .
- CIt has an inverse, .
- DIt has an inverse, .
- EIt has no inverse.

**Q2: **

Find the inverse of the following matrix.

- A
- B
- C
- D
- E

**Q3: **

Use technology to find the inverse of the following matrix.

- A
- B
- C
- D
- E

**Q4: **

Use technology to find the inverse of the following matrix.

- A
- B
- C
- D
- E

**Q5: **

Use technology to find the inverse of the following matrix.

- A
- B
- C
- D
- E

**Q6: **

Using the elementary row operation, find for the given matrix if possible.

- A
- B
- C
- D
- E The matrix has no inverse.

**Q7: **

Using the Cayley-Hamilton theorem, find for the given matrix if possible.

- A
- B
- C
- D
- EThe matrix has no inverse.

**Q8: **

Using elementary row operations, find for the given matrix if possible.

- A
- B
- C
- D The matrix has no inverse.
- E

**Q9: **

Find the multiplicative inverse of

- A
- B
- C
- D

**Q10: **

Find the multiplicative inverse of the matrix

- A
- B
- C
- D

**Q11: **

Find the multiplicative inverse of the matrix

- A
- B
- C
- D

**Q12: **

Consider the matrix Find its inverse, given that it has the form , where , , and are numbers that you should find.

- A
- B
- C
- D
- E

**Q13: **

Consider the matrix Find its inverse, given that it has the form where , , , , , and are numbers you should find.

- A
- B
- C
- D