Lesson Worksheet: Inverse of a 2 × 2 Matrix Mathematics

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 31−31 invertible?

  • AYes
  • BNo

Q2:

Is the matrix 31−3−1 invertible?

  • AYes
  • BNo

Q3:

Is the matrix 51−15 invertible?

  • AYes
  • BNo

Q4:

Given that the matrix 71−7𝑎 is invertible, what must be true of 𝑎.

  • A𝑎≠−1
  • B𝑎≠7
  • C𝑎≠1
  • D𝑎≠−7
  • E𝑎≠0

Q5:

Find the set of real values of 𝑎 for which 𝑎𝑖−𝑖1 has a multiplicative inverse, where 𝑖=−1.

  • Aℝ−{0}
  • Bℝ
  • Cℝ−{1}
  • Dℝ−{−1}

Q6:

Find the set of real values of 𝑥 for which −4𝑥68−17𝑥 has no multiplicative inverse.

  • Aℝ−{−17}
  • B{−17,17}
  • C−174,174
  • Dℝ−{17}
  • Eℝ−174

Q7:

Find the value of 𝑥 that makes the matrix 𝑥−8−5−1 singular.

Q8:

Find the inverse of the matrix 𝐴=4−237.

  • A𝐴=134−43−2−7
  • B𝐴=1347−234
  • C𝐴=122−43−2−7
  • D𝐴=12272−34
  • E𝐴=13472−34

Q9:

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

  • A5𝑏≠2𝑎
  • B𝑎≠𝑏
  • C2𝑏≠5𝑎
  • D2𝑏=5𝑎
  • E2𝑎+5𝑏≠0

Q10:

Which of the following matrices is singular?

  • A9−797
  • B−9−797
  • C−9797
  • D−9−7−97

Q11:

Find all the values of 𝑥 for which the matrix 𝑥−11515𝑥+11 is singular.

  • A196
  • B14,−14
  • C5,−5
  • D4

Q12:

Are the matrices 12377−2−31, 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 (𝑥)−382(𝑥)+3 singular.

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

Q15:

Find the inverse of the following matrix. 𝐴=−11−18

  • A𝐴=19−8−1−1−1
  • B𝐴=17−81−11
  • C𝐴=178−11−1
  • D𝐴=19−81−11
  • E𝐴=198−11−1

Q16:

Find the inverse of the matrix 𝐴=3316.

  • A𝐴=1216−3−13
  • B𝐴=115−313−6
  • C𝐴=1156313
  • D𝐴=121−313−6
  • E𝐴=1156−3−13

Q17:

Find the multiplicative inverse of the matrix 𝐴=−4−1035, if possible.

  • A𝐴has no multiplicative inverse.
  • B−410−35
  • C⎡⎢⎢⎢⎣121−310−25⎤⎥⎥⎥⎦
  • D510−3−4
  • E5−103−4

Q18:

Find the multiplicative inverse of 690069.

  • A−6900−69
  • B⎡⎢⎢⎣16900169⎤⎥⎥⎦
  • C⎡⎢⎢⎣−16900−169⎤⎥⎥⎦
  • D6900−69

Q19:

Given 𝐴=4−7−3−4, find its multiplicative inverse if possible.

  • A−137−4734
  • B−137−4374
  • C−4734
  • D𝐴 has no multiplicative inverse.

Q20:

Find the multiplicative inverse of 𝐴=−48−1224, if possible.

  • A𝐴has no multiplicative inverse.
  • B2412−8−4
  • C−11922412−8−4
  • D−119224−812−4

Q21:

Given that 𝐵=−2−5−6−10,𝐴×𝐵=𝐼, find the matrix 𝐴.

  • A⎡⎢⎢⎣1−12−3515⎤⎥⎥⎦
  • B⎡⎢⎢⎣1512351⎤⎥⎥⎦
  • C−1056−2
  • D−10−5−6−2

Q22:

Given that 𝐴=𝑥−𝑥𝑦0𝑦, find 𝐴.

  • A⎡⎢⎢⎢⎣1𝑥101𝑦⎤⎥⎥⎥⎦
  • B⎡⎢⎢⎢⎣1𝑥−101𝑦⎤⎥⎥⎥⎦
  • C⎡⎢⎢⎢⎣−1𝑥01−1𝑦⎤⎥⎥⎥⎦
  • D⎡⎢⎢⎢⎣1𝑥011𝑦⎤⎥⎥⎥⎦

Q23:

Find the multiplicative inverse of 𝜃𝜃1𝜃.sectansec

  • A𝜃−1−𝜃𝜃sectansec
  • B𝜃−𝜃−1𝜃sectansec
  • C𝜃𝜃𝜃−1tansecsec
  • D𝜃𝜃1𝜃sectansec

Q24:

Find the multiplicative inverse of 𝜃−𝜃𝜃𝜃.sincoscossin

  • A𝜃−𝜃𝜃𝜃cossinsincos
  • B−𝜃𝜃−𝜃−𝜃cossinsincos
  • C𝜃−𝜃𝜃𝜃sincoscossin
  • D𝜃𝜃−𝜃𝜃sincoscossin

Q25:

Consider the matrices 𝐴 and 𝐵. Determine (𝐴+𝐵)𝐴=−3−2−5−7,𝐵=−1289.

  • A0.500.375−0.25
  • B30−42
  • C−4032
  • D−0.2500.3750.5

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