Question

The matrix

\[ A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \]

is:

• A. Unit Matrix
• B. Diagonal Matrix
• C. Symmetric Matrix
• D. Skew Symmetric Matrix

Hint:

A matrix is symmetric if it is equal to its transpose, i.e., \( A = A^T \).

Answer 1

The Correct Option is C

Step 1: Definition of matrix types.

A unit matrix is a square matrix where all diagonal elements are 1 and all other elements are 0.
A diagonal matrix is a square matrix where all elements outside the main diagonal are zero.
A symmetric matrix is a square matrix that is equal to its transpose, i.e., \( A = A^T \).
A skew-symmetric matrix is a square matrix where \( A^T = -A \).

Step 2: Checking symmetry of matrix \( A \).

The given matrix is:

\[ A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \]

The transpose of \( A \) is:

\[ A^T = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \]

Since \( A^T = A \), the matrix satisfies the definition of a symmetric matrix.

Step 3: Conclusion.

The matrix \( A \) is a symmetric matrix.