Algebra

Matrices & Determinants

Medium

applied

If $A = \begin{bmatrix} 0 & a & 2 \\ -2 & 0 & b \\ -2 & 2 & c \end{bmatrix}$ is a skew symmetric matrix, then the value of $(a + b + c)^3$ is

✅ Correct Option: 2

A matrix $A$ is skew-symmetric if $A^T = -A$ .

This means:

All diagonal elements must be 0
Elements satisfy $a_{ij} = -a_{ji}$

For the given matrix $A = \begin{bmatrix} 0 & a & 2 \\ -2 & 0 & b \\ -2 & 2 & c \end{bmatrix}$ , the diagonal elements are $0, 0, c$ .

Since all diagonal elements must be 0:

$c = 0$

Comparing positions $(1,2)$ and $(2,1)$ :

Position $(1,2) = a$
Position $(2,1) = -2$

Using the property $a_{12} = -a_{21}$ :

$a = -(-2)$

$a = 2$

Comparing positions $(2,3)$ and $(3,2)$ :

Position $(2,3) = b$
Position $(3,2) = 2$

Using the property $a_{23} = -a_{32}$ :

$b = -(2)$

$b = -2$

The values are:

$a = 2$

$b = -2$

$c = 0$

Therefore:

$a + b + c = 2 + (-2) + 0$

$a + b + c = 0$

$(a + b + c)^3 = 0^3$

$(a + b + c)^3 = 0$

2023: 30 May Shift 3

If a, b and c are all different from zero and $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$ , then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is :

2026: 22 May Shift 2

If $f(x) = \begin{vmatrix} 0 & x+a & x+b \\ x-a & 0 & x+c \\ x-b & x-c & 0 \end{vmatrix}$ then the value of $f(0)$ is equal to:

2025: 21 May Shift 2

If $x, y$ and $z$ are non-zero distinct numbers, then $\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}$ is equal to

2026: 25 May Shift 1

If $P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}$ and $P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}$ , then the value of $x$ and $y$ respectively are

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:

2025: 16 May Shift 1

Match List-I with List-II

List-I	List-II
(Matrix A)	(Determinant of adj A)
(A) $\begin{bmatrix} 2 & 1 \\ -1 & 2 \end{bmatrix}$	(I) 3
(B) $\begin{bmatrix} 3 & 4 \\ 3 & 6 \end{bmatrix}$	(II) 6
(C) $\begin{bmatrix} 3 & 7 \\ -2 & -4 \end{bmatrix}$	(III) 5
(D) $\begin{bmatrix} 4 & 3 \\ 3 & 3 \end{bmatrix}$	(IV) 2

Choose the correct answer from the options given below:

If A=[0a2−20b−22c]A = \begin{bmatrix} 0 & a & 2 \\ -2 & 0 & b \\ -2 & 2 & c \end{bmatrix}A=​0−2−2​a02​2bc​​ is a skew symmetric matrix, then the value of (a+b+c)3(a + b + c)^3(a+b+c)3 is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} 0 & a & 2 \\ -2 & 0 & b \\ -2 & 2 & c \end{bmatrix}$ is a skew symmetric matrix, then the value of $(a + b + c)^3$ is