GATE AI 2025 | Linear Algebra Question 4 | Discrete Mathematics | GATE Data Science and Artificial Intelligence

GATE AI 2025

MCQ (Single Correct Answer)

-0

Let $A \in \mathbb{R}^{n \times n}$ be such that $A^3=A$. Which one of the following statements is ALWAYS correct?

$A$ is invertible

Determinant of $A$ is 0

The sum of the diagonal elements of $A$ is 1

A and $A^2$ have the same rank

GATE AI 2025

MCQ (More than One Correct Answer)

-0

An $n \times n$ matrix $A$ with real entries satisfies the property: $\|A x\|^2=\|x\|^2$ for all $x \in R^n$ where $\|\cdot\|$ denotes the Euclidean norm. Which of the following statements is/are ALWAYS correct?

$A$ must be orthogonal

$A=I$, where $I$ denotes the identity matrix, is the only solution

The eigenvalues of $A$ are either +1 or $-1$

A has full rank

GATE Data Science and Artificial Intelligence Subjects

Browse all chapters by subject

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Discrete Mathematics

Linear Algebra Graph Theory Mathematical Logic Probability Calculus

Artificial Intelligence

Machine Learning

Database Management System and Warehousing

Functional Dependencies and Normalization Structured Query Language Relational Algebra

Python Programming

Data Structures

Hashing

Algorithms

Searching and Sorting Greedy Method Complexity Analysis and Asymptotic Notations