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

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:

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

  • AYes
  • BNo

Q4:

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

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

Q5:

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

  • A𝑎1
  • B𝑎7
  • C𝑎1
  • D𝑎7
  • E𝑎0

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=3257,𝐵=1289.

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

Q8:

Find the multiplicative inverse of 𝜃𝜃𝜃𝜃.sincoscossin

  • A𝜃𝜃𝜃𝜃cossinsincos
  • B𝜃𝜃𝜃𝜃cossinsincos
  • C𝜃𝜃𝜃𝜃sincoscossin
  • D𝜃𝜃𝜃𝜃sincoscossin

Q9:

Given that 𝐴=𝑥𝑥𝑦0𝑦, find 𝐴.

  • A1𝑥101𝑦
  • B1𝑥101𝑦
  • C1𝑥011𝑦
  • D1𝑥011𝑦

Q10:

Using matrix inverses, solve the following for 𝑋: 𝑋3243=0230.

  • A𝑋=8696
  • B𝑋=6698
  • C𝑋=8696
  • D𝑋=8696
  • E𝑋=8696

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