Algebra

Matrices & Determinants

Easy

common

The area (in sq. units) of the triangle whose vertices are $(0, 0)$ , $(a, 0)$ , $(0, b)$ , is equal to

$a^2$

$|ab|$

$\frac{1}{2}|ab|$

$b^2$

✅ Correct Option: 3

The triangle has vertices at $(0, 0)$ , $(a, 0)$ , and $(0, b)$ .

The point $(0, 0)$ is at the origin.

The point $(a, 0)$ lies on the x-axis at distance $|a|$ from the origin.

The point $(0, b)$ lies on the y-axis at distance $|b|$ from the origin.

This forms a right-angled triangle with the right angle at the origin.

The base of the triangle is $|a|$ units.

The height of the triangle is $|b|$ units.

Absolute values are used since $a$ and $b$ can be negative, but distances are always positive.

Area $= \dfrac{1}{2} \times \text{base} \times \text{height}$

Area $= \dfrac{1}{2} \times |a| \times |b|$

Area $= \dfrac{1}{2}|ab|$

Therefore, the area of the triangle is $\dfrac{1}{2}|ab|$ square units.

2023: 23 May Shift 3

Let $A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}$ , then adjoint (A) is:

2025: 30 May Shift 1

Let $A = [a_{ij}]_{2 \times 4}$ and $B = [b_{ij}]_{4 \times 2}$ , then $|3AB|$ is equal to

2025: 29 May Shift 2

Which of the following statement are correct?

(A) $A = [a_{ij}]_{n \times n}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$

(B) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$

(D) For every square matrix $A$ , there exist an identity matrix of the same order such that $IA = AI = I$

Choose the correct answer from the options given below:

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $A$ is a square matrix of order $3$ and $\lvert 2A \rvert = k\lvert A \rvert$ , then $k$ is	(I) $0$
(B) Value of $\begin{vmatrix}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{vmatrix}$ is	(II) $3$
(C) Matrix $\begin{bmatrix}5-x & x+1 \\ 2 & 4\end{bmatrix}$ is singular, then $x =$	(III) $8$
(D) If $A = (a_{ij}) = \begin{bmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{bmatrix}$ , then the minor of the element $a_{23}$ is	(IV) $7$

Choose the correct answer from the options given below :

2025: 16 May Shift 1

Which of the following are correct?

(A) For a square matrix A, if A³ = I, then A⁻¹ = A².

(B) The determinant of only a square matrix can be defined.

(D) If A and B are two non-singular matrices of the same order, then (AB)⁻¹ = B⁻¹A⁻¹.

Choose the correct answer from the options given below:

2026: 25 May Shift 1

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. If A is an invertible square matrix then $\lvert A^{-1}\rvert =$	I. $\dfrac{1}{\lvert A\rvert}(\mathrm{adj}\,A)$
B. For every square matrix (adj A) A =	II. $\dfrac{1}{\lvert A\rvert}$
C. For a square matrix A, if $\lvert A\rvert \neq 0$ , then $A^{-1} =$	III. $B^{-1}A^{-1}$
D. If A and B are invertible matrices, then $(AB)^{-1} =$	IV. $\lvert A\rvert.I$ , where I is the identity matrix of same order as A

Choose the correct answer from the options given below:

The area (in sq. units) of the triangle whose vertices are (0,0)(0, 0)(0,0), (a,0)(a, 0)(a,0), (0,b)(0, b)(0,b), is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The area (in sq. units) of the triangle whose vertices are $(0, 0)$ , $(a, 0)$ , $(0, b)$ , is equal to