# Worksheet: Finding the Inverse of a 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 no inverse.
• BIt has an inverse, .
• CIt has an inverse, .
• DIt has an inverse, .
• EIt has an inverse, .

Q2:

Find the inverse of the following matrix.

• A
• B
• C
• D
• E

Q3:

Determine whether the matrix has an inverse by finding whether the determinant is nonzero. If the determinant is nonzero, find the inverse using the inverse formula involving the cofactor matrix.

• AThe matrix has no inverse.
• BIt has an inverse, which is .
• CIt has an inverse, which is .
• DIt has an inverse, which is .
• EIt has an inverse, which is .

Q4:

Find, if it exists, the inverse of the matrix

• A
• B
• C
• D
• E

Q5:

Use technology to find the inverse of the following matrix.

• A
• B
• C
• D
• E

Q6:

Use technology to find the inverse of the following matrix.

• A
• B
• C
• D
• E

Q7:

Use technology to find the inverse of the following matrix.

• A
• B
• C
• D
• E

Q8:

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

• AThe matrix has no inverse.
• B
• C
• D
• E

Q9:

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

• AThe matrix has no inverse.
• B
• C
• D
• E

Q10:

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

• A
• B
• CThe matrix has no inverse.
• D
• E