# Worksheet: Inverse and Power of Diagonal Matrices

In this worksheet, we will practice finding the inverse of a diagonal matrix and determining the value of a diagonal matrix raised to a high power.

**Q1: **

Find for the matrix using elementary row operations.

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**Q2: **

Given that , find .

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**Q3: **

Given that , find .

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**Q4: **

Given the matrix , find .

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**Q5: **

Find the result of raising the matrix to the power of 3.

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**Q6: **

Given the matrix , find .

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**Q7: **

Fill in the blank: If is a diagonal matrix of size that has no inverse, then .

- Amatrix has at least one zero diagonal element
- Bmatrix has at least two diagonal elements that are multiplicative inverses of each other
- Cmatrix has at least two diagonal elements that are additive inverses of each other
- Dmatrix has identical diagonal elements

**Q8: **

Fill in the blank: If , then .

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**Q9: **

If matrix is diagonal and it has a zero diagonal element, is it invertible?

- AYes
- BNo

**Q10: **

Fill in the blank: If , then .

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**Q11: **

Given , find .

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