Standard result: if ∣A∣=0, the system AX=B has a unique solution. Option 3 claims that ∣A∣=0 with (adjA)B=0 gives no solution, which contradicts uniqueness. So option 3 is the incorrect statement.
Which one of the following options is incorrect? For a square matrix A in the matrix equation AX = B.
CUET UG 2023 — Mathematics Algebra
2023mcqmedium
Which one of the following options is incorrect?
For a square matrix A in the matrix equation AX = B.
Official previous-year question
Held on 23 May 2023 · Verified 13 Jul 2026.
Options
- A
If ∣A∣=0, then there exists a unique solution
- B
If ∣A∣=0 and (adj A)B = 0 then there is no solution
- C
If ∣A∣=0 and (adj A)B = 0 then there is no solution
- D
If ∣A∣=0 and (adj A)B = 0 then system has infinitely many solutions
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