The portal has been deactivated. Please contact your portal admin.

Lesson Worksheet: Power of a Matrix Mathematics • 10th Grade

In this worksheet, we will practice using the matrix multiplication to determine the square and cube of a square matrix.


Given that ๐ด=๏”โˆ’61โˆ’55๏ , find ๐ด๏Šจ.

  • A๏”31โˆ’1520๏ 
  • B๏”37353550๏ 
  • C๏”315โˆ’120๏ 
  • D๏”61โˆ’31โˆ’3126๏ 


Consider ๐‘‹=๏”โˆ’3โˆ’35โˆ’6๏ ,๐‘Œ=๏”136โˆ’6๏ . What is ๐‘‹โˆ’๐‘Œ๏Šจ๏Šจ?

  • A๏”โˆ’2557โˆ’30โˆ’33๏ 
  • B๏”โˆ’25โˆ’1542โˆ’33๏ 
  • C๏”โˆ’2542โˆ’15โˆ’33๏ 
  • D๏”โˆ’25โˆ’3057โˆ’33๏ 


Given the matrix ๐ด=๏”40โˆ’37๏ , calculate ๐ดโˆ’3๐ด๏Šฉ๏Šจ.

  • A๏”160โˆ’378196๏ 
  • B๏”480โˆ’246294๏ 
  • C๏”160โˆ’180196๏ 
  • D๏”480โˆ’312294๏ 


Consider the matrix ๐ด=๏˜112101210๏ค.

Find ๐ด๏Šจ.

  • A๐ด=๏˜114101410๏ค๏Šจ
  • B๐ด=๏˜114101410๏ค๏Šจ
  • C๐ด=๏˜633322325๏ค๏Šจ
  • D๐ด=๏˜633312315๏ค๏Šจ
  • E๐ด=๏˜224202420๏ค๏Šจ

Find ๐ด๏Šฉ.

  • A๐ด=๏˜336303630๏ค๏Šฉ
  • B๐ด=๏˜159159581588๏ค๏Šฉ
  • C๐ด=๏˜336303630๏ค๏Šฉ
  • D๐ด=๏˜159159581588๏ค๏Šฉ
  • E๐ด=๏˜118101810๏ค๏Šฉ


For ๐ด=๏”4โˆ’54โˆ’5๏ , write ๐ด๏Šจ as a multiple of ๐ด.

  • A4๐ด
  • B๐ด
  • Cโˆ’4๐ด
  • Dโˆ’๐ด
  • E2๐ด


If ๐ด=๏”0220๏ , which of the following is ๐ด๏Šฏ๏Šฏ?

  • A2๏”0220๏ ๏Šง๏Šฆ๏Šฆ
  • B2๏”1001๏ ๏Šฏ๏Šฏ
  • C2๏”0220๏ ๏Šฏ๏Šฏ
  • D2๏”0220๏ ๏Šฏ๏Šฎ
  • E2๏”1001๏ ๏Šฏ๏Šฎ


Which of the following statements is true for all ๐‘›ร—๐‘› matrices ๐ด and ๐ต?

  • A๐ด๐ต=๐ด(๐ด๐ต)๐ต๏Šจ๏Šจ
  • B(๐ดโˆ’๐ต)=๐ดโˆ’2๐ด๐ต+๐ต๏Šจ๏Šจ๏Šจ
  • C(๐ด๐ต)=๐ด๐ต๏Šจ๏Šจ๏Šจ
  • D(๐ด+๐ต)(๐ดโˆ’๐ต)=๐ดโˆ’๐ต๏Šจ๏Šจ
  • E(๐ด+๐ต)=๐ด+2๐ด๐ต+๐ต๏Šจ๏Šจ๏Šจ


Fill in the blank: If ๐ด=๏”403โˆ’4๏ , then ๐ด=๏Šซ๏Šฆ.

  • A2๏”1001๏ ๏Šญ๏Šซ
  • B2๏”1001๏ ๏Šซ๏Šฆ
  • C2๏”1001๏ ๏Šง๏Šฆ๏Šฆ
  • D2๏”1001๏ ๏Šจ๏Šซ


Given that ๐‘€=๏”56โˆ’5โˆ’4๏ , find the values of ๐‘ฅ and ๐‘ฆ that satisfy ๐‘€+๐‘ฅ๐‘€+๐‘ฆ๐ผ=๐‘‚๏Šจ, where ๐‘‚ is the zero matrix of order 2ร—2 and ๐ผ is the unit matrix of order 2ร—2.

  • A๐‘ฅ=โˆ’1, ๐‘ฆ=10
  • B๐‘ฅ=โˆ’1, ๐‘ฆ=0
  • C๐‘ฅ=โˆ’11, ๐‘ฆ=0
  • D๐‘ฅ=โˆ’11, ๐‘ฆ=10


Consider the matrices ๐ด=๏”0โˆ’421๏ ,๐ต=๏”โˆ’3โˆ’766โˆ’43๏ ,๐ถ=๏˜77โˆ’72โˆ’77๏ค. Determine the matrix ๐‘‹ that satisfies โˆ’๐‘‹=๐ด+(๐ต๐ถ)๏Œณ๏Šจ๏Œณ.

  • A๏”22โˆ’51โˆ’3โˆ’48๏ 
  • B๏”22โˆ’9โˆ’45โˆ’48๏ 
  • C๏”22โˆ’3โˆ’51โˆ’48๏ 
  • D๏”22โˆ’45โˆ’9โˆ’48๏ 

This lesson includes 32 additional questions and 225 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.