Algebra

Matrices & Determinants

Medium

applied

For a matrix $A = \begin{bmatrix} a & -1 & b \\ -2 & 1 & -1 \\ 1 & 0 & 2 \end{bmatrix}$ , $C_{32} = -1$ and $C_{33} = 3$ , where $C_{ij}$ is the cofactor of element $a_{ij}$ in $A$ . Then

$a=5\ \&\ b=2$

$a=5\ \&\ b=3$

$a=2\ \&\ b=5$

$a=3\ \&\ b=5$

✅ Correct Option: 2

$C_{33}=\begin{vmatrix}a&-1\\-2&1\end{vmatrix}=a-2=3$ , so $a=5$ .

$C_{32}=-\begin{vmatrix}a&b\\-2&-1\end{vmatrix}=a-2b=-1$ , so $5-2b=-1$ and $b=3$ .

2026: 22 May Shift 1

Let $A$ be a matrix given by $A=[a_{ij}]_{3\times3}$ , $a_{ij}=i+j$ , then

Match List-I with List-II

List-I	List-II
(A) Number of the elements in $A$	(I) 3
(B) Sum of the diagonal elements	(II) 9
(C) $a_{31}+a_{32}-a_{33}$	(III) -1
(D) Cofactor of $a_{13}$	(IV) 12

Choose the correct answer from the options given below:

2026: 26 May Shift 2

If $\begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix} = (x^{\lambda}-1)^{\mu}$ then the value of $\lambda$ and $\mu$ are given by

2025: 15 May Shift 1

If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to

2025: 30 May Shift 2

If the system of equations

$x - 3y + 5z = 3$

$x - 2y + 4z = 4$

$2x - 7y + \lambda z = 5$

has infinite number of solutions, then the value of $\lambda$ is:

2025: 29 May Shift 2

If the system of equation

$x - y + z = 4$

$x - 2y - 2z = 9$

$2x + y + \lambda z = 1$

has a unique solution, then

2026: 29 May Shift 2

If A is a skew symmetric matrix, then $A^2$ is a

For a matrix A=[a−1b−21−1102]A = \begin{bmatrix} a & -1 & b \\ -2 & 1 & -1 \\ 1 & 0 & 2 \end{bmatrix}A=​a−21​−110​b−12​​, C32=−1C_{32} = -1C32​=−1 and C33=3C_{33} = 3C33​=3, where CijC_{ij}Cij​ is the cofactor of element aija_{ij}aij​ in AAA. Then

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

For a matrix $A = \begin{bmatrix} a & -1 & b \\ -2 & 1 & -1 \\ 1 & 0 & 2 \end{bmatrix}$ , $C_{32} = -1$ and $C_{33} = 3$ , where $C_{ij}$ is the cofactor of element $a_{ij}$ in $A$ . Then