Lesson Worksheet: Inverse of a 2 × 2 Matrix Mathematics • 10th Grade

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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:

Are the matrices 1234,⎡⎢⎢⎣1121314⎤⎥⎥⎦ multiplicative inverses of each other?

  • AYes
  • BNo

Q4:

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

Q5:

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

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

Q6:

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}

Q7:

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

Q8:

Find the multiplicative inverse of 𝜃−𝜃𝜃𝜃.sincoscossin

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

Q9:

Given that 𝐴=𝑥−𝑥𝑦0𝑦, find 𝐴.

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

Q10:

Using matrix inverses, solve the following for 𝑋: 𝑋−324−3=0−230.

  • A𝑋=8696
  • B𝑋=66−9−8
  • C𝑋=−86−9−6
  • D𝑋=8−69−6
  • E𝑋=86−9−6

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