Applied Mathematics

Algebra

Easy

If a matrix A is both symmetric and skew symmetric then :

A is a diagonal matrix

A is a zero matrix

A is a scalar matrix

A is a square matrix

✅ Correct Option: 2

Symmetric: $A = A^T$ . Skew-symmetric: $A = -A^T$ . Both together imply $A = -A$ , so $2A = 0$ and $A$ is the zero matrix.

2026: 14 May Shift 2

A and B are square matrices of order 3 each such that $|A|=3, |B|=2$ , then the value of $|4AB|$ will be?

2023: 11 Aug Shift 1

The least positive integer X satisfying $28 \equiv x (\mod 6)$ is :

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. A matrix that has unequal number of rows and columns is called	I. Non-singular matrix
B. A matrix whose determinant is non-zero is called	II. Null matrix
C. A diagonal matrix whose diagonal elements are equal is called	III. Rectangular matrix
D. A matrix that is both symmetric and skew-symmetric is	IV. Scalar matrix

Choose the correct answer from the options given below:

2023: 22 May Shift 3

If the matrix $\begin{bmatrix} 0 & 2 & 5x \\ -2 & 0 & 6 \\ 10 & -6 & y \end{bmatrix}$ is skew-symmetric matrix, then the value of $(y - 4x)$ is :

2026: 14 May Shift 2

If A is a non-singular square matrix of order n, then which of the following are TRUE ?

A. $|adj A|=|A|^{n-1}$

B. $|adj A|=|A|^{n-2}$

C. $|adj (adj A)|=|A|^{(n-2)^2}$

D. $|adj (adj A)|=|A|^{(n-1)^2}$

Choose the correct answer from the options given below:

2023: 11 Aug Shift 1

The area of the triangle with vertices $(1,4), (2,7)$ and $(4,13)$ is :

Solution