Matrix Relations Workbook - Levels 1 & 2
Instructions: Multiple-correct unless stated otherwise.
LEVEL 1 (Q1-Q10)
Q1. A^2=B^2, |A+B|≠0. (A) A=B (B) A=-B (C) |A-B|=0 (D) AB=BA
Q2. AB=0, |A|≠0. (A) B=0 (B) BA=0 (C) |B|=0 (D) AB=BA
Q3. A^2=I. (A) A invertible (B) A^-1=A (C) |A|=±1 (D) A+I invertible
Q4. A^3=B^3 and |A^2+AB+B^2|≠0. Choose correct.
Q5. AB=BA, A^2=B^2, |A+B|≠0. Choose correct.
Q6. A^2=0. (A) A singular (B) |A|=0 (C) A invertible (D) rank(A)=3
Q7. AB=I. (A) BA=I (B) both invertible (C) |A||B|=1 (D) rank(A)=rank(B)
Q8. A^2=A. (A) idempotent (B) A-I invertible (C) eigenvalues only 0,1 (D) |A|=1
Q9. A^2=-I. (A) invertible (B) A^-1=-A (C) |A|=0 (D) A^4=I
Q10. AB=BA and A^2+B^2=2AB. Choose correct.
LEVEL 2 (Q11-Q20)
Q11. A^4=B^4, |A^2+B^2|≠0. Choose correct.
Q12. A^4=B^4, AB=BA, |A+B|≠0.
Q13. A^3B=B^3A and A^3=B^3.
Q14. A^5=B^5, A^4B=B^4A, A≠B. (A)|A^4+B^4|=0 (B)|A+B|=0 (C)A-B singular (D)A^5+B^5 singular
Q15. A^2B=AB^2, |A+B|≠0.
Q16. A^6=B^6, |A^3+B^3|≠0.
Q17. A^3=I. Determine true statements about invertibility and determinant.
Q18. A^4+B^4=0. Determine necessary conclusions.
Q19. (A+B)^2=(A-B)^2. Choose correct.
Q20. A^2=B^2=C^2 and A+B+C invertible. Determine relations.
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