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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