68 free MCQs on Matrices, each with its own worked answer and explanation. Matrix operations, determinants, inverses, and solving linear systems
Take the timed Matrices chapterwise test →68 practice questions on Matrices, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Matrices notes.
Element aij of matrix A sits at the intersection of row i and column j.
Q1.
A matrix with equal number of rows and columns is called a:
Q2.
The order of a matrix with 3 rows and 4 columns is:
Q3.
For a 2x2 matrix [[a,b],[c,d]], the determinant is:
Q4.
A square matrix in which all elements except the main diagonal are zero is called a:
Q5.
The identity matrix of order 3 has main diagonal elements equal to:
Q6.
If A is a matrix of order 2 x 3, what is the order of A<sup>T</sup>?
Q7.
The transpose of a matrix A is obtained by:
Q8.
A matrix in which all elements are zero is called a:
Q9.
Two matrices can be added only if they have:
Q10.
If A has order m x n and B has order n x p, then AB has order:
Q11.
A symmetric matrix satisfies:
Q12.
The determinant of the identity matrix I<sub>n</sub> is:
Q13.
A square matrix A is called singular if:
Q15.
A skew-symmetric matrix satisfies:
Q16.
The number of elements in a matrix of order m x n is:
Q19.
A matrix with only one column is called a:
Q20.
The matrix [[1,0,0],[0,2,0],[0,0,3]] is an example of a:
Q21.
For a 3x3 matrix A, det(2A) =
Q22.
If A is an n x n matrix, det(A<sup>T</sup>) =
Q23.
The sum of two matrices is defined only when they have the same:
Q24.
For the product AB to be defined, the number of columns of A must equal the number of ___ of B:
Q25.
The product of a 2×3 matrix and a 3×2 matrix has order:
Q26.
A matrix with an equal number of rows and columns is called a ___ matrix:
Q27.
A matrix in which every element is zero is called a ___ matrix:
Q28.
The identity matrix has 1s along the ___ and 0s elsewhere:
Q29.
The transpose of a matrix is obtained by interchanging its:
Q30.
If A has order 3×4, then its transpose Aᵀ has order:
Q31.
A square matrix A is called symmetric if:
Q32.
A square matrix A is called skew-symmetric if:
Q33.
The diagonal elements of a skew-symmetric matrix are all:
Q34.
Matrix multiplication is, in general:
Q37.
Because A + B = B + A for matrices, matrix addition is:
Q38.
A diagonal matrix has non-zero entries only on its:
Q39.
A scalar matrix is a diagonal matrix whose diagonal elements are all:
Q40.
The additive identity for matrices of a given order is the:
Q41.
The eigenvalues of a real symmetric matrix are always:
Q42.
The Vandermonde determinant for distinct values (a, b, c) equals:
Q43.
The null space (kernel) of matrix A consists of all vectors x such that:
Q44.
If A is a 3x3 matrix with rank 2, the null space of A has dimension:
Q45.
For a Hermitian matrix H, the defining property is:
Q46.
The sum of eigenvalues of matrix A = [[3,1],[2,2]] equals:
Q47.
Schur decomposition states that every square matrix A can be written as A = QTQ<sup>-1</sup> where:
Q48.
A square matrix A is invertible if and only if:
Q49.
The inverse of a matrix A is given by A⁻¹ = (adj A) divided by:
Q50.
For invertible matrices A and B, (AB)⁻¹ equals:
Q52.
If A is a 2×2 matrix with |A| = 3, then |A⁻¹| equals:
Q53.
A square matrix A satisfying A² = A is called:
Q54.
A square matrix A satisfying AᵀA = I is called:
Q55.
The trace of a square matrix is the sum of its:
Q56.
If A and B are both symmetric matrices of the same order, then A + B is:
Q57.
Every square matrix can be written uniquely as the sum of a symmetric matrix and a:
Q58.
A square matrix A for which Aᵏ = 0 for some positive integer k is called:
Q59.
The product of a square matrix and its inverse is the:
Q60.
The number of elements on the main diagonal of a 3×3 matrix is:
Q61.
If A is a 3×3 matrix with det(A) = 2, then det(2A) equals:
Q62.
A matrix that is both symmetric and skew-symmetric must be:
Q63.
For a 3×3 matrix A with det(A) = 5, det(adj A) equals:
Q64.
If a square matrix A satisfies A² = A and A ≠ I, then det(A) equals:
Q65.
The inverse of the matrix [[2, 3], [1, 2]] is:
Q67.
For A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]], the trace of AB is:
Q68.
If a square matrix A satisfies A² = 0, then (I − A)⁻¹ equals:
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