Worksheet: Properties of Inverse Matrices

In this worksheet, we will practice using some properties of matrix inverse.

Q1:

If 𝐴 is a matrix, which of the following is equal to ο€Ήπ΄ο…οŠ±οŠ§οŠ¨?

  • A𝐴
  • B𝐴
  • Cο€Ήπ΄ο…οŠ±οŠ§οŽ οŽ‘
  • Dο€Ήπ΄ο…οŠ¨οŠ±οŠ§

Q2:

Consider the matrix 𝐴=ο”βˆ’31βˆ’25. Find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • A3βˆ’12βˆ’5
  • BβŽ‘βŽ’βŽ’βŽ£βˆ’513113βˆ’213313⎀βŽ₯βŽ₯⎦
  • Cο”βˆ’52βˆ’13
  • DβŽ‘βŽ’βŽ’βŽ£βˆ’313213βˆ’113513⎀βŽ₯βŽ₯⎦
  • Eο”βˆ’31βˆ’25

Q3:

If 𝐴 and 𝐡 are both nonsingular matrices, then what is the value of (𝐴𝐡)?

  • A𝐴𝐡
  • B(𝐡𝐴)
  • Cβˆ’π΄π΅
  • D𝐡𝐴

Q4:

If 𝐼 is the identity matrix, which of the following is equal to 𝐼?

  • A0110
  • B𝐼
  • C1111
  • Dβˆ’πΌ

Q5:

Given that 𝐴=ο”βˆ’6βˆ’21βˆ’3, find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • Aο”βˆ’6βˆ’21βˆ’3
  • Bο”βˆ’3βˆ’12βˆ’6
  • Cο”βˆ’31βˆ’2βˆ’6
  • Dο”βˆ’62βˆ’1βˆ’3

Q6:

Given that (𝐴𝐡)=165βˆ’3βˆ’3321𝐴=ο”βˆ’2βˆ’1βˆ’3βˆ’2,, determine 𝐡.

  • A213335
  • Bο”βˆ’9βˆ’1βˆ’3βˆ’1
  • CβŽ‘βŽ’βŽ’βŽ£βˆ’161612βˆ’32⎀βŽ₯βŽ₯⎦
  • Dο”βˆ’113βˆ’9

Q7:

Given that 𝐴=52βˆ’6βˆ’5𝐡=ο”βˆ’22βˆ’42,, find 𝐡𝐴.

  • A⎑⎒⎒⎣9267268131126⎀βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎣1126726813926⎀βŽ₯βŽ₯⎦
  • CβŽ‘βŽ’βŽ’βŽ£βˆ’926βˆ’726βˆ’813βˆ’1126⎀βŽ₯βŽ₯⎦
  • DβŽ‘βŽ’βŽ’βŽ£βˆ’1126βˆ’726βˆ’813βˆ’926⎀βŽ₯βŽ₯⎦

Q8:

If 𝐴 is a matrix, which of the following is equal to ο€Ήπ΄ο…οŠ±οŠ§ο?

  • Aο€Ήπ΄ο…οοŠ±οŠ§
  • Bπ΄οŽ ο‘‰
  • Cο€Ήπ΄ο…οŠ±οŠ§οŽ ο‘‰
  • D𝐴
  • E𝐴

Q9:

Consider the matrix 𝐴=ο”βˆ’6βˆ’120. Find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • A61βˆ’20
  • B012βˆ’1βˆ’3ο₯
  • C0βˆ’216
  • D31βˆ’120ο₯
  • Eο”βˆ’6βˆ’120

Q10:

Consider the matrix 𝐴=ο”βˆ’5βˆ’462. Find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • A54βˆ’6βˆ’2
  • B⎑⎒⎒⎣1727βˆ’37βˆ’514⎀βŽ₯βŽ₯⎦
  • Cο”βˆ’2βˆ’645
  • D⎑⎒⎒⎣51437βˆ’27βˆ’17⎀βŽ₯βŽ₯⎦
  • Eο”βˆ’5βˆ’462

Q11:

Consider the matrix 𝐴=ο”βˆ’5βˆ’13βˆ’2. Find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • A51βˆ’32
  • BβŽ‘βŽ’βŽ’βŽ£βˆ’213113βˆ’313βˆ’513⎀βŽ₯βŽ₯⎦
  • C2βˆ’315
  • D⎑⎒⎒⎣513313βˆ’113213⎀βŽ₯βŽ₯⎦
  • Eο”βˆ’5βˆ’13βˆ’2

Q12:

Given that 𝐴=ο”βˆ’7βˆ’2βˆ’16, find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • Aο”βˆ’7βˆ’2βˆ’16
  • B612βˆ’7
  • C6βˆ’1βˆ’2βˆ’7
  • Dο”βˆ’7216

Q13:

Given that 𝐴=ο”βˆ’2βˆ’54βˆ’1, find ο€Ήπ΄ο…οŠ±οŠ§οŠ±οŠ§.

  • Aο”βˆ’2βˆ’54βˆ’1
  • Bο”βˆ’1βˆ’45βˆ’2
  • Cο”βˆ’14βˆ’5βˆ’2
  • Dο”βˆ’25βˆ’4βˆ’1

Q14:

Determine whether the following statement is true or false: If 𝐴 exists, then detdet𝐴=(𝐴).

  • Afalse
  • Btrue

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