The matrix \(\begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}\) is a:
(A) scalar matrix
(B) diagonal matrix
(C) skew-symmetric matrix
(D) symmetric matrix
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
The given matrix is the identity matrix I of order 3. In it:
\(a_{ij} = 0 \text{ for } i \ne j\)
\(a_{11} = a_{22} = a_{33} = 1\)
\(I' = I\)
So the matrix has all off-diagonal entries 0, all diagonal entries equal to 1 (not 0), and equals its own transpose.
Checking the statements
(A) scalar matrix — Correct. It is diagonal with all diagonal entries equal (to 1).
(B) diagonal matrix — Correct. Every off-diagonal entry is 0.
(C) skew-symmetric matrix — Incorrect. A skew-symmetric matrix has every diagonal entry 0; here they are 1.
(D) symmetric matrix — Correct. \(I' = I\).