Question

If \[ A= \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] then $A$ is:

• A. Singular matrix
• B. Identity matrix
• C. Null matrix
• D. Skew-symmetric matrix

Hint:

Identity matrix acts like the number $1$ in matrix multiplication: \[ AI=IA=A \] for every compatible matrix $A$.

Answer 1

The Correct Option is B

Concept: An identity matrix is a square matrix in which:
• All diagonal elements are $1$.
• All non-diagonal elements are $0$. For order $2$: \[ I= \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]

Step 1: Observe the given matrix carefully.
Given: \[ A= \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] The diagonal entries are: \[ 1,1 \] and all off-diagonal entries are: \[ 0 \]

Step 2: Compare with standard matrices.
This exactly matches the definition of the identity matrix: \[ I_2= \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] Hence, \[ A=I_2 \] Therefore, \[ \boxed{\text{Identity matrix}} \]