alleryIf $A$ is a $3\times3$ matrix with $|A| = 4$, then $|2A|$ equals:
- 32
- 8
- 64
- 16
Show answer and solution
Correct answer: A. 32
For an n×n matrix, |kA| = kⁿ|A|.
Here n=3, k=2 ⟹ |2A| = 8·4 = 32.
GRE Determinants — practice questions
Explore 22 free Determinants questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Determinants with Quill →Determinants questions and exercises with answers
Showing questions 1–22 of 22.
If $A$ is a $3\times3$ matrix with $|A| = 4$, then $|2A|$ equals:Read the answer and worked solution →The area of the triangle with vertices $(3,8)$, $(-4,2)$ and $(5,1)$ is:Read the answer and worked solution →Three points are collinear if and only if the determinant formed from their coordinates is:Read the answer and worked solution →If $A$ is a $3\times3$ matrix with $|A| = 5$, then $|\,\text{adj}\,A\,|$ equals:Read the answer and worked solution →For a square matrix $A$ of order $n$, the product $A\,(\text{adj}\,A)$ equals:Read the answer and worked solution →A square matrix $A$ is invertible if and only if:Read the answer and worked solution →If $A$ and $B$ are $3\times3$ matrices with $|A| = 2$ and $|B| = 3$, then $|AB|$ equals:Read the answer and worked solution →The value of the determinant $\begin{vmatrix} 2 & 4 \\ 3 & 5 \end{vmatrix}$ is:Read the answer and worked solution →The matrix $\begin{bmatrix} k & 2 \\ 3 & 4 \end{bmatrix}$ is singular when $k$ equals:Read the answer and worked solution →A system of linear equations $AX = B$ (with $A$ square) has a unique solution if and only if:Read the answer and worked solution →If $|A| = 4$ for an invertible matrix $A$, then $|A^{-1}|$ equals:Read the answer and worked solution →The value of $\begin{vmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{vmatrix}$ is:Read the answer and worked solution →If $A$ is a $3\times3$ matrix with $|A| = 2$, then $|3A|$ equals:Read the answer and worked solution →The transpose of $A^T$ is:Read the answer and worked solution →For matrices A (3×2) and B (2×4), the product AB has order:Read the answer and worked solution →The transpose of the product (AB)^T equals:Read the answer and worked solution →Matrix multiplication is:Read the answer and worked solution →The determinant of the 2×2 matrix [[a, b], [c, d]] equals:Read the answer and worked solution →A matrix A has an INVERSE if and only if:Read the answer and worked solution →By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:Read the answer and worked solution →For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:Read the answer and worked solution →An ORTHOGONAL matrix A satisfies:Read the answer and worked solution →
Worked practice questions
The area of the triangle with vertices $(3,8)$, $(-4,2)$ and $(5,1)$ is:
- 15.25 sq units
- 30.5 sq units
- 25 sq units
- 61 sq units
Show answer and solution
Correct answer: B. 30.5 sq units
Area = ½|3(2−1) + (−4)(1−8) + 5(8−2)| = ½|3 + 28 + 30| = ½·61 = 30.5 sq units.
Three points are collinear if and only if the determinant formed from their coordinates is:
- negative
- one
- zero
- undefined
Show answer and solution
Correct answer: C. zero
The area determinant of three collinear points is zero, since they form no triangle.
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