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Which of the following matrices is an orthogonal matrix? (2021)

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Question: Which of the following matrices is an orthogonal matrix? (2021)

Options:

  1. A matrix whose transpose is equal to its inverse
  2. A matrix with all elements equal
  3. A matrix with only one row
  4. A matrix with all diagonal elements equal

Correct Answer: A matrix whose transpose is equal to its inverse

Exam Year: 2021

Solution: 

An orthogonal matrix is defined as a matrix whose transpose is equal to its inverse.

Which of the following matrices is an orthogonal matrix? (2021)

Practice Questions

Q1
Which of the following matrices is an orthogonal matrix? (2021)
  1. A matrix whose transpose is equal to its inverse
  2. A matrix with all elements equal
  3. A matrix with only one row
  4. A matrix with all diagonal elements equal

Questions & Step-by-Step Solutions

Which of the following matrices is an orthogonal matrix? (2021)
  • Step 1: Understand what an orthogonal matrix is. An orthogonal matrix is a square matrix whose rows and columns are orthogonal unit vectors.
  • Step 2: Know the definition of the transpose of a matrix. The transpose of a matrix is obtained by flipping it over its diagonal, turning rows into columns and vice versa.
  • Step 3: Know the definition of the inverse of a matrix. The inverse of a matrix A is another matrix, denoted as A^-1, such that when A is multiplied by A^-1, the result is the identity matrix.
  • Step 4: To check if a matrix is orthogonal, calculate its transpose and its inverse.
  • Step 5: Compare the transpose and the inverse. If they are equal, the matrix is orthogonal.
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