Matrices MCQs Math

\[
\textbf{MCQs on Matrices with Answers}
\]

\[
\textbf{Q1: What is the dimension of a matrix with 3 rows and 4 columns?}
\]
\[
\text{(A) } 3 \times 3 \quad \text{(B) } 4 \times 3 \quad \text{(C) } 3 \times 4 \quad \text{(D) } 4 \times 4
\]
\[
\textbf{Answer: (C) } 3 \times 4
\]

\[
\textbf{Q2: If a matrix has 5 rows and 2 columns, what type of matrix is it?}
\]
\[
\text{(A) Square Matrix} \quad \text{(B) Row Matrix} \quad \text{(C) Column Matrix} \quad \text{(D) Rectangular Matrix}
\]
\[
\textbf{Answer: (D) Rectangular Matrix}
\]

\[
\textbf{Q3: What is the determinant of a \( 2 \times 2 \) identity matrix?}
\]
\[
\text{(A) } 0 \quad \text{(B) } 1 \quad \text{(C) } -1 \quad \text{(D) } Undefined
\]
\[
\textbf{Answer: (B) } 1
\]

\[
\textbf{Q4: If a matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), then what is the transpose of \( A \)?}
\]
\[
\text{(A) } \begin{pmatrix} 1 & 3 \\ 2 & 4 \end{pmatrix} \quad
\text{(B) } \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad
\text{(C) } \begin{pmatrix} 4 & 3 \\ 2 & 1 \end{pmatrix} \quad
\text{(D) } \begin{pmatrix} -1 & -2 \\ -3 & -4 \end{pmatrix}
\]
\[
\textbf{Answer: (A) } \begin{pmatrix} 1 & 3 \\ 2 & 4 \end{pmatrix}
\]

\[
\textbf{Q5: If \( A \) is a \( 2 \times 3 \) matrix and \( B \) is a \( 3 \times 2 \) matrix, what is the dimension of \( AB \)?}
\]
\[
\text{(A) } 2 \times 2 \quad \text{(B) } 3 \times 3 \quad \text{(C) } 3 \times 2 \quad \text{(D) } 2 \times 3
\]
\[
\textbf{Answer: (A) } 2 \times 2
\]

\[
\textbf{Q6: What is a matrix called if all its elements are zero?}
\]
\[
\text{(A) Zero Matrix} \quad \text{(B) Scalar Matrix} \quad \text{(C) Identity Matrix} \quad \text{(D) Diagonal Matrix}
\]
\[
\textbf{Answer: (A) Zero Matrix}
\]

\[
\textbf{Q7: Which of the following is a diagonal matrix?}
\]
\[
\text{(A) } \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad
\text{(B) } \begin{pmatrix} 5 & 0 \\ 0 & 6 \end{pmatrix} \quad
\text{(C) } \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \quad
\text{(D) } \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}
\]
\[
\textbf{Answer: (B) } \begin{pmatrix} 5 & 0 \\ 0 & 6 \end{pmatrix}
\]

\[
\textbf{Q8: Which operation is not defined for two matrices \( A \) and \( B \)?}
\]
\[
\text{(A) Addition if dimensions are same} \quad
\text{(B) Multiplication if columns of \( A \) equal rows of \( B \)} \quad
\text{(C) Transpose of a matrix} \quad
\text{(D) Division of one matrix by another}
\]
\[
\textbf{Answer: (D) Division of one matrix by another}
\]

\[
\textbf{Q9: What is the rank of the zero matrix of any dimension?}
\]
\[
\text{(A) Zero} \quad \text{(B) One} \quad \text{(C) Equal to number of rows} \quad \text{(D) Undefined}
\]
\[
\textbf{Answer: (A) Zero}
\]

\[
\textbf{Q10: For a square matrix \( A \), if \( A = A^T \), what type of matrix is \( A \)?}
\]
\[
\text{(A) Symmetric Matrix} \quad \text{(B) Skew-Symmetric Matrix} \quad \text{(C) Identity Matrix} \quad \text{(D) Diagonal Matrix}
\]
\[
\textbf{Answer: (A) Symmetric Matrix}
\]