Which one of the following options is incorrect? For a square matrix A in the matrix equation AX = B. Option 1: If, A, ≠ 0, then there exists a unique solution Option 2: If, A, = 0 and (adj A)B ≠ 0 then there is no solution Option 3: If, A, ≠ 0 and (adj A)B ≠ 0 then there is no solution Option 4: If, A, = 0 and (adj A)B = 0 then system has infinitely many solutions

Answer: If, A, ≠ 0 and (adj A)B ≠ 0 then there is no solution. Solution: Standard result: if, A, 0, the system AX = B has a unique solution. Option 3 claims that, A, 0 with (adj A)B 0 gives no solution, which contradicts uniqueness. So option 3 is the incorrect statement.

Algebra

Matrices & Determinants

Medium

core

Which one of the following options is incorrect?

For a square matrix A in the matrix equation AX = B.

If $|A| \neq 0$ , then there exists a unique solution

If $|A| = 0$ and (adj A)B $\neq$ 0 then there is no solution

If $|A| \neq 0$ and (adj A)B $\neq$ 0 then there is no solution

If $|A| = 0$ and (adj A)B = 0 then system has infinitely many solutions

✅ Correct Option: 3

Standard result: if $|A| \ne 0$ , the system $AX = B$ has a unique solution. Option 3 claims that $|A| \ne 0$ with $(\text{adj}\,A)B \ne 0$ gives no solution, which contradicts uniqueness. So option 3 is the incorrect statement.

2026: 18 May Shift 2

If matrix $A=\begin{bmatrix} 5 & 2 & 3 \\ 4 & 1 & 2 \\ 7 & 6 & 0 \end{bmatrix}$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$16$
B.	Minor of $a_{23}$	II.	$27$
C.	Cofactor of $a_{32}$	III.	$19$
D.	If $a_{23}$ is interchanged with $a_{32}$ , then $\vert A \vert$	IV.	$2$

Choose the correct answer from the options given below:

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If $\begin{bmatrix}3 & 1\\2 & 1\end{bmatrix}P\begin{bmatrix}2 & 1\\3 & 2\end{bmatrix}=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ then matrix P is

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The number of all possible matrices of order $2 \times 3$ with entries -1 or 1 is

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The equations in terms of $x$ and $y$ are:

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The system of equations $3x + 4y = 5$ , $6x + 7y = -8$ is written in matrix form as

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Which of the following is NOT correct?

Which one of the following options is incorrect? For a square matrix A in the matrix equation AX = B.

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Which one of the following options is incorrect?

For a square matrix A in the matrix equation AX = B.