Question

\(\text{The matrix }\) \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \text{ is a:}\)
(A) Scalar matrix
(B) Diagonal matrix
(C) Skew-symmetric matrix
(D) Symmetric matrix

• A. (A), (B), and (D) only
• B. (A), (B), and (C) only
• C. (A), (B), (C), and (D)
• D. (B), (C), and (D) only

Answer 1

The Correct Option is A

\(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}\)
- The matrix above is a scalar matrix because all diagonal elements are equal and non-zero.
- It is also a diagonal matrix since all non-diagonal elements are zero.
- This matrix is symmetric because \( A = A^T \), where \( A^T \) is the transpose of \( A \).
- However, it is not a skew-symmetric matrix because a skew-symmetric matrix requires all diagonal elements to be zero.