Algebra

Matrices & Determinants

Hard

core

The value of $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is negative, if

Values of $a,b,c$ are distinct positive.

Values of $a,b,c$ are negative

Values of $a,b,c$ are equal

Value of any 2 are positive and the third is negative

✅ Correct Option: 1

Expanding gives $-(a^3+b^3+c^3-3abc)=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ . For distinct positive $a,b,c$ the first factor is positive and the second, being half the sum of squared differences, is also positive, so the determinant is negative.

2025: 13 May Shift 1

If A and B are invertible matrices of same order, then which one of the following is NOT true?

2026: 12 May Shift 2

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ , then $A^2 - 5A$ is equal to : (where $I_2$ is identity matrix of order 2)

2026: 21 May Shift 1

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$ , then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

2026: 15 May Shift 1

If $A = [a_{ij}]_{3\times3}$ is a square matrix, where $a_{ij} = i - j + 3$ , then the value of $a_{21} + a_{31} - a_{23}$ is

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:

2025: 13 May Shift 2

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then $A^{-1}$ is equal to

The value of ∣abcbcacab∣\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}​abc​bca​cab​​ is negative, if

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is negative, if