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WorksheetsMatrix Theory Quiz
Total questions: 46
Worksheet time: 23mins
If a matrix A has 3 rows and 5 columns, then the order of A is:
5×3
3×5
8×1
15×1
What is the total number of elements in a 4×3 matrix?
7
12
16
10
If A is a 2×3 matrix and B is a 3×4 matrix, the product AB is:
3×3
2×3
2×4
Not defined
Which of the following is true for the diagonal elements of an identity matrix?
All are zero
All are one
Alternates between 1 and 0
Depends on matrix size
The transpose of a 2×3 matrix is of order:
2×3
3×3
3×2
1×6
If A = [1 2; 3 4], then A(1,2) refers to:
1
3
2
4
A matrix having only one column is called:
Row matrix
Null matrix
Square matrix
Column matrix
Which of the following matrices has equal number of rows and columns?
Row matrix
Column matrix
Square matrix
Rectangular matrix
If matrix A is 3×2 and matrix B is 2×3, what is the order of AB?
2×2
3×2
3×3
2×3
Which of the following operations is not defined for two matrices of different orders?
Transpose
Addition
Scalar multiplication
Determinant
A matrix with all elements zero is called:
Null matrix
Identity matrix
Unit matrix
Diagonal matrix
Which matrix has all its off-diagonal elements zero?
Diagonal matrix
Scalar matrix
Row matrix
Echelon matrix
Which matrix is always symmetric?
Any square matrix
Identity matrix
Diagonal matrix
Column matrix
A skew-symmetric matrix must have:
a_ij = a_ji
a_ij = -a_ji
a_ij = 0
Only diagonal entries
Which of the following is always square?
Echelon matrix
Identity matrix
Row matrix
Column matrix
The diagonal elements of a skew-symmetric matrix are always:
1
0
Negative
2
In echelon form, the leading entry of each row:
is always 1
appears to the right of the leading entry in the row above
is zero
is less than the one above
Which of the following matrices is both symmetric and skew-symmetric?
Identity matrix
Any scalar matrix
Null matrix
Diagonal matrix
A square matrix is symmetric if:
A^T = A
A^T = -A
A^2 = I
A = A^-1
Which matrix remains unchanged after transposition?
Skew-symmetric
Diagonal
Symmetric
Row
A matrix whose elements are all 1 is known as:
One matrix
Identity matrix
Diagonal matrix
Unity matrix
The row echelon form ensures that:
All rows are identical
Each leading coefficient is right of the one in the row above
All rows are zero
Matrix is symmetric
Which matrix is always invertible?
Identity
Zero
Skew-symmetric
Diagonal with 0
If A = -Aᵗ, then A is:
Symmetric
Diagonal
Skew-symmetric
Echelon
If A and B are of the same order, then (A - B)ᵗ equals:
Aᵗ - Bᵗ
A - B
B - A
Aᵗ + Bᵗ
Which operation is not defined for matrix A (2×3) and matrix B (3×2)?
AB
BA
A + B
Transpose of AB
Matrix multiplication is:
Commutative
Always defined
Not necessarily commutative
Distributive over transpose
The scalar multiplication of a matrix multiplies:
Only diagonal elements
Only rows
Every element
Only columns
The inverse of a matrix exists only if:
Matrix is rectangular
Matrix is square and non-singular
Matrix is singular
Matrix has determinant zero
Which of the following is correct regarding matrix subtraction?
It is associative
It is not defined for different orders
Always results in zero matrix
Commutative
If A is a matrix, then (Aᵗ)ᵗ equals:
A
Aᵗ
A + Aᵗ
A - Aᵗ
The product of a matrix and its inverse is:
Zero matrix
Identity matrix
Transpose
Negative of the matrix
If A is a 3×3 invertible matrix, then A⁻¹ exists and satisfies:
AA⁻¹ = 0
AA⁻¹ = A
AA⁻¹ = I
A⁻¹A = A
To find inverse using elementary transformations, the original matrix is augmented with:
Null matrix
Ones matrix
Identity matrix
Transpose
Matrix multiplication is:
Associative
Commutative
Reflexive
Idempotent
Which of the following is true for scalar multiplication?
Scalar multiplies only rows
Scalar multiplies diagonals only
Scalar multiplies all entries
None of the above
The sum of a matrix and its transpose is symmetric if the matrix is:
Skew-symmetric
Symmetric
Square
Diagonal
The inverse of a diagonal matrix exists if all diagonal elements are:
Zero
Positive
Non-zero
Integer
Transpose of the identity matrix is:
Zero matrix
Same identity matrix
Skew-symmetric
Diagonal with negative values
Which operation is not applicable to a 2×2 matrix?
Transpose
Finding inverse
Scalar multiplication
Cross product
The inverse of a matrix A is found using:
AB = A
AAᵗ = A
AA⁻¹ = I
A² = I
Which of the following is true for symmetric matrix A?
A = -A
A = Aᵗ
A = I
A = 0
If A = [2 4; 1 3], then Aᵗ is:
[2 1; 4 3]
[1 2; 3 4]
[4 2; 3 1]
[2 4; 3 1]
Which matrix has determinant always 1?
Identity matrix
Skew-symmetric
Null matrix
Echelon matrix
A scalar matrix is a:
Square matrix with all elements equal
Diagonal matrix with equal diagonal entries
Skew-symmetric
Matrix of all 1s
Inverse of a matrix A is denoted by:
Aᵗ
-A
A⁻¹
A⁰
