Ten multiple-choice questions on matrix dimensions, addition, scalar multiplication, products, determinants and inverses. Choose the best answer, then read the explanation to see the typical mistake. Each question has exactly one correct option.
PrecalculusCommon Core: N-VM.C.6 · N-VM.C.7 · N-VM.C.8 · N-VM.C.9 · N-VM.C.10
🎯 Matrices and Matrix Operations – Precalculus math quiz
Question 1
A matrix with three rows and two columns.
What are the dimensions of this matrix?
A
\(2\times 3\)
B
\(3\times 2\)
C
\(6\times 1\)
D
\(3\times 3\)
Question 2
A 2 × 3 matrix.
What is the entry in row 2, column 3?
A
\(8\)
B
\(1\)
C
\(-2\)
D
\(-4\)
Question 3
Which pair of matrices can be added?
A
a \(2\times 3\) and a \(3\times 2\) matrix
B
a \(2\times 2\) and a \(3\times 3\) matrix
C
a \(1\times 3\) and a \(3\times 1\) matrix
D
a \(2\times 3\) and a \(2\times 3\) matrix
Question 4
Matrix A.
What is the sum of all four entries of \(2A\)?
A
\(6\)
B
\(12\)
C
\(9\)
D
\(24\)
Question 5
Matrices A and B.
What is the entry in row 1, column 1 of \(AB\)?
A
\(10\)
B
\(12\)
C
\(16\)
D
\(13\)
Question 6
A \(2\times 3\) matrix is multiplied by a \(3\times 4\) matrix. What are the dimensions of the product?
A
\(3\times 3\)
B
\(2\times 3\)
C
\(2\times 4\)
D
\(3\times 4\)
Question 7
Which statement is true for every \(2\times 2\) matrix \(A\) and the identity matrix \(I\)?
A
\(AI=A\)
B
\(AB=BA\) for every matrix \(B\)
C
\(AO=A\) for the zero matrix \(O\)
D
\(A+I=A\)
Question 8
A 2 × 2 matrix.
What is the determinant of this matrix?
A
\(18\)
B
\(42\)
C
\(-18\)
D
\(11\)
Question 9
For which value of \(k\) does the matrix with top row \(k,3\) and bottom row \(4,6\) fail to have an inverse?
A
\(k=-2\)
B
\(k=2\)
C
\(k=12\)
D
\(k=\frac{1}{2}\)
Question 10
A 2 × 2 matrix with determinant 1.
What is the entry in row 1, column 2 of the inverse of this matrix?
A
\(1\)
B
\(2\)
C
\(-1\)
D
\(-2\)
🎉 Quiz complete!
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Remember:
- An \(m\times n\) matrix has \(m\) rows and \(n\) columns; entry \(a_{ij}\) sits in row \(i\), column \(j\).
- Add or subtract matrices only when dimensions match; scalar multiplication scales every entry.
- \(AB\) exists when columns of \(A\) equal rows of \(B\), and in general \(AB\neq BA\).
- \(A+O=A\) and \(AI=IA=A\) for the zero matrix \(O\) and identity matrix \(I\).
- For a 2 × 2 matrix, \(\det A=ad-bc\), and \(A^{-1}\) exists exactly when \(\det A\neq 0\).
See every chapter on the Precalculus math page.