# Worksheet: Inverse of a 2x2 Matrix

In this worksheet, we will practice checking whether a 2x2 matrix has an inverse and then finding its inverse, if possible.

Q1:

Find the inverse of the matrix .

• A
• B
• C
• D
• E

Q2:

Find the inverse of the matrix .

• A
• B
• C
• D
• E

Q3:

Is the matrix invertible?

• AYes
• BNo

Q4:

Is the matrix invertible?

• AYes
• BNo

Q5:

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

• A
• B
• C
• D
• E

Q6:

Given that find .

• A
• B
• C
• D

Q7:

Are the matrices multiplicative inverses of each other?

• AYes
• BNo

Q8:

Find the inverse of the following matrix.

• A
• B
• C
• D
• E

Q9:

Find the multiplicative inverse of the matrix , if possible.

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

Q10:

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

• A
• B
• C
• D
• E

Q11:

Find the multiplicative inverse of , if possible.

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

Q12:

Given find its multiplicative inverse if possible.

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

Q13:

Find the multiplicative inverse of .

• A
• B
• C
• D

Q14:

Given that find the matrix .

• A
• B
• C
• D

Q15:

Find the multiplicative inverse of

• A
• B
• C
• D

Q16:

Find the multiplicative inverse of

• A
• B
• C
• D

Q17:

Find the multiplicative inverse of the matrix , if possible.

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

Q18:

Find the multiplicative inverse of the matrix , if possible.

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

Q19:

Is there any value of for which the matrix has no inverse?

• Ayes, when
• Bno
• Cyes, when
• Dyes, when
• Eyes, when

Q20:

Is there any value of for which the matrix has no inverse?

• Ayes, when
• Byes, when
• Cno
• Dyes, the matrix has no inverse for all values of
• Eyes, when

Q21:

Under what condition on is the matrix invertible?

• A or
• B is any real number.
• C and
• D or
• E and

Q22:

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

• A
• B
• C
• D

Q23:

Find the value of that makes the matrix singular.

Q24:

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

• A
• B
• C
• D
• E

Q25:

Under what condition on and is the matrix invertible?

• A
• B
• C
• D
• E