The matrix X such that it satisfies the equation: Xbmatrix 3 & 2 \\ 1 & -1 bmatrix = bmatrix 4 & 1 \\ 2 & 3 bmatrix is Option 1: bmatrix -1 & 1 \\ 1 & 1 bmatrix Option 2: bmatrix -1 & 0 \\ 1 & -1 bmatrix Option 3: bmatrix -1 & 1 \\ -1 & 1 bmatrix Option 4: bmatrix 1 & 1 \\ 1 & -1 bmatrix

Answer: bmatrix 1 & 1 \\ 1 & -1 bmatrix. Solution: Post-multiply by the inverse: X = bmatrix 4 & 1 \\ 2 & 3 bmatrixA^(-1) where A = bmatrix 3 & 2 \\ 1 & -1 bmatrix and, A, = -5. Computing gives X = bmatrix 1 & 1 \\ 1 & -1 bmatrix, which can be verified by direct multiplication.

Algebra

Matrices & Determinants

Medium

core

The matrix X such that it satisfies the equation: $X\begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$ is

$\begin{bmatrix} -1 & 1 \\ 1 & 1 \end{bmatrix}$

$\begin{bmatrix} -1 & 0 \\ 1 & -1 \end{bmatrix}$

$\begin{bmatrix} -1 & 1 \\ -1 & 1 \end{bmatrix}$

$\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$

✅ Correct Option: 4

Post-multiply by the inverse: $X = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}A^{-1}$ where $A = \begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix}$ and $|A| = -5$ . Computing gives $X = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$ , which can be verified by direct multiplication.

2026: 21 May Shift 1

For any invertible matrix $A$ , which of the following is NOT true.

2025: 3 June Shift 1

If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$ , then

Match List-I with List-II

List-I	List-II
(A) det (A)	(I) $-\frac{1}{3}$
(B) det $(A^{-1})$	(II) $-12$
(C) det (2A)	(III) $-3$
(D) det $(3A^T)$	(IV) $-27$

Choose the correct answer from the options given below:

2026: 26 May Shift 2

If A is a square matrix of order 3 such that $|A| = 3$ , then the value of $|adj\,A| + |adj\,(adj\,A)|$ is

2026: 18 May Shift 2

If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$ , where $m$ is a positive integer then which of the following are factors of $k$ ?

A. $m!$

B. $(m+1)!$

C. $(m+2)!$

D. $(m+3)!$

Choose the correct answer from the options given below:

2025: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) A square matrix $P$ is said to be non-singular if	(I) $\vert P\vert = 0$
(B) A square matrix $P$ is said to be singular if	(II) $P P^T$ is symmetric
(C) If a matrix $P$ is both symmetric and skew-symmetric, then	(III) $\vert P\vert \neq 0$
(D) If $P$ is a square matrix, then	(IV) $P$ is a null matrix

Choose the correct answer from the options given below:

2026: 21 May Shift 2

The matrix $A = \begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$ is a

A. Symmetric matrix

B. Scalar matrix

C. Diagonal matrix

D. Skew-symmetric matrix

Choose the correct answer from the options given below:

The matrix X such that it satisfies the equation: X[321−1]=[4123]X\begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}X[31​2−1​]=[42​13​] is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The matrix X such that it satisfies the equation: $X\begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$ is