# Worksheet: Inverse of a 2 × 2 Matrix

In this worksheet, we will practice checking whether a 2 × 2 matrix has an inverse and then finding its inverse, if possible.

Q1:

Is the matrix invertible?

• AYes
• BNo

Q2:

Is the matrix invertible?

• AYes
• BNo

Q3:

Is the matrix invertible?

• AYes
• BNo

Q4:

Given that the matrix is invertible, what must be true of .

• A
• B
• C
• D
• E

Q5:

Find the set of real values of for which has a multiplicative inverse, where .

• A
• B
• C
• D

Q6:

Find the set of real values of for which has no multiplicative inverse.

• A
• B
• C
• D
• E

Q7:

Find the value of that makes the matrix singular.

Q8:

Find the inverse of the matrix .

• A
• B
• C
• D
• E

Q9:

Under what condition on and is the matrix invertible?

• A
• B
• C
• D
• E

Q10:

Which of the following matrices is singular?

• A
• B
• C
• D

Q11:

Find all the values of for which the matrix is singular.

• A196
• B
• C
• D4

Q12:

Are the matrices multiplicative inverses of each other?

• AYes
• BNo

Q13:

Are the matrices multiplicative inverses of each other?

• AYes
• BNo

Q14:

Find the set of real values of that make the matrix singular.

• A
• B
• C
• D

Q15:

Find the inverse of the following matrix.

• A
• B
• C
• D
• E

Q16:

Find the inverse of the matrix .

• A
• B
• C
• D
• E

Q17:

Find the multiplicative inverse of the matrix , if possible.

• Ahas no multiplicative inverse.
• B
• C
• D
• E

Q18:

Find the multiplicative inverse of .

• A
• B
• C
• D

Q19:

Given find its multiplicative inverse if possible.

• A
• B
• C
• D has no multiplicative inverse.

Q20:

Find the multiplicative inverse of , if possible.

• Ahas no multiplicative inverse.
• B
• C
• D

Q21:

Given that find the matrix .

• A
• B
• C
• D

Q22:

Given that find .

• A
• B
• C
• D

Q23:

Find the multiplicative inverse of

• A
• B
• C
• D

Q24:

Find the multiplicative inverse of

• A
• B
• C
• D

Q25:

Consider the matrices and . Determine

• A
• B
• C
• D