CUET Mathematics 2024 - The matrix [arraylll1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1array] is a : (A) scalar matrix (B) diagonal matrix (C) skew-symmetric matix (D) symmetric matrix Choose the correct answer from the options given below : | PYQs + Solutions

CUET Mathematics 2024

Algebra

Matrices & Determinants

Easy

The matrix $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$ is a : $\newline$ (A) scalar matrix $\newline$ (B) diagonal matrix $\newline$ (C) skew-symmetric matix $\newline$ (D) symmetric matrix
Choose the correct answer from the options given below :

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(B), (C) and (D) only

✅ Correct Option: 1

A scalar matrix has all diagonal elements equal to the same value, with zeros elsewhere. In our matrix, all diagonal elements are

1

and all off-diagonal elements are

0

, so it is a scalar matrix.

A diagonal matrix has non-zero elements only on the main diagonal. Hence, it is also a diagonal matrix.

A skew-symmetric matrix satisfies

A^T = -A

The transpose of our matrix is itself:

\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]

The negative of our matrix is:

\left[\begin{array}{lll}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{array}\right]

Since the transpose ≠ negative, it is not skew-symmetric.

A symmetric matrix satisfies

A^T = A

Since the transpose equals the original matrix, it is symmetric.