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 3131 invertible?

  • AYes
  • BNo

Q2:

Is the matrix 3131 invertible?

  • AYes
  • BNo

Q3:

Is the matrix 5115 invertible?

  • AYes
  • BNo

Q4:

Given that the matrix 717𝑎 is invertible, what must be true of 𝑎.

  • A𝑎1
  • B𝑎7
  • C𝑎1
  • D𝑎7
  • E𝑎0

Q5:

Find the set of real values of 𝑎 for which 𝑎𝑖𝑖1 has a multiplicative inverse, where 𝑖=1.

  • A{0}
  • B
  • C{1}
  • D{1}

Q6:

Find the set of real values of 𝑥 for which 4𝑥6817𝑥 has no multiplicative inverse.

  • A{17}
  • B{17,17}
  • C174,174
  • D{17}
  • E174

Q7:

Find the value of 𝑥 that makes the matrix 𝑥851 singular.

Q8:

Find the inverse of the matrix 𝐴=4237.

  • A𝐴=1344327
  • B𝐴=1347234
  • C𝐴=1224327
  • D𝐴=1227234
  • E𝐴=1347234

Q9:

Under what condition on 𝑎 and 𝑏 is the matrix 𝑎2𝑏5 invertible?

  • A5𝑏2𝑎
  • B𝑎𝑏
  • C2𝑏5𝑎
  • D2𝑏=5𝑎
  • E2𝑎+5𝑏0

Q10:

Which of the following matrices is singular?

  • A9797
  • B9797
  • C9797
  • D9797

Q11:

Find all the values of 𝑥 for which the matrix 𝑥11515𝑥+11 is singular.

  • A196
  • B14,14
  • C5,5
  • D4

Q12:

Are the matrices 12377231, multiplicative inverses of each other?

  • AYes
  • BNo

Q13:

Are the matrices 1234,1121314 multiplicative inverses of each other?

  • AYes
  • BNo

Q14:

Find the set of real values of (𝑥) that make the matrix 𝑥382𝑥+3 singular.

  • A{5,5}
  • B{6,4}
  • C{4,6}
  • D{7,7}

Q15:

Find the inverse of the following matrix. 𝐴=1118

  • A𝐴=198111
  • B𝐴=178111
  • C𝐴=178111
  • D𝐴=198111
  • E𝐴=198111

Q16:

Find the inverse of the matrix 𝐴=3316.

  • A𝐴=1216313
  • B𝐴=1153136
  • C𝐴=1156313
  • D𝐴=1213136
  • E𝐴=1156313

Q17:

Find the multiplicative inverse of the matrix 𝐴=41035, if possible.

  • A𝐴has no multiplicative inverse.
  • B41035
  • C12131025
  • D51034
  • E51034

Q18:

Find the multiplicative inverse of 690069.

  • A690069
  • B16900169
  • C16900169
  • D690069

Q19:

Given 𝐴=4734, find its multiplicative inverse if possible.

  • A1374734
  • B1374374
  • C4734
  • D𝐴 has no multiplicative inverse.

Q20:

Find the multiplicative inverse of 𝐴=481224, if possible.

  • A𝐴has no multiplicative inverse.
  • B241284
  • C1192241284
  • D1192248124

Q21:

Given that 𝐵=25610,𝐴×𝐵=𝐼, find the matrix 𝐴.

  • A1123515
  • B1512351
  • C10562
  • D10562

Q22:

Given that 𝐴=𝑥𝑥𝑦0𝑦, find 𝐴.

  • A1𝑥101𝑦
  • B1𝑥101𝑦
  • C1𝑥011𝑦
  • D1𝑥011𝑦

Q23:

Find the multiplicative inverse of 𝜃𝜃1𝜃.sectansec

  • A𝜃1𝜃𝜃sectansec
  • B𝜃𝜃1𝜃sectansec
  • C𝜃𝜃𝜃1tansecsec
  • D𝜃𝜃1𝜃sectansec

Q24:

Find the multiplicative inverse of 𝜃𝜃𝜃𝜃.sincoscossin

  • A𝜃𝜃𝜃𝜃cossinsincos
  • B𝜃𝜃𝜃𝜃cossinsincos
  • C𝜃𝜃𝜃𝜃sincoscossin
  • D𝜃𝜃𝜃𝜃sincoscossin

Q25:

Consider the matrices 𝐴 and 𝐵. Determine (𝐴+𝐵)𝐴=3257,𝐵=1289.

  • A0.500.3750.25
  • B3042
  • C4032
  • D0.2500.3750.5

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