Two matrices A and B can be added if
A
They are square
B
They have same order
C
They are diagonal
D
They are invertible
Analysis & Theory
Matrix addition is possible only if both matrices have the same order.
If A is m×n and B is n×p, then the product AB is of order
A
m×p
B
n×m
C
p×n
D
m×n
Analysis & Theory
If A is m×n and B is n×p, then AB is defined and has order m×p.
Matrix multiplication is
A
Always commutative
B
Not always commutative
C
Always associative and commutative
D
None of these
Analysis & Theory
In general, AB ≠ BA, so matrix multiplication is not commutative.
Which property holds for matrix multiplication?
A
Associative law
B
Distributive law
C
Both associative and distributive
D
Commutative law
Analysis & Theory
Matrix multiplication is associative and distributive over addition, but not commutative.
The transpose of a product of two matrices satisfies
A
(AB)^T = A^T B^T
B
(AB)^T = B^T A^T
C
(AB)^T = A B
D
(AB)^T = B A
Analysis & Theory
Transpose of product: (AB)^T = B^T A^T.
If A is a square matrix, then (A^T)^T equals
A
A
B
A^T
C
A^2
D
I
Analysis & Theory
Taking transpose twice gives back the original matrix: (A^T)^T = A.
For any two matrices A and B, (A+B)^T equals
A
A^T + B^T
B
A^T - B^T
C
A^T B^T
D
None
Analysis & Theory
Transpose distributes over addition: (A+B)^T = A^T + B^T.
If A is invertible, then (A^−1)^−1 equals
A
A^−2
B
A
C
A^T
D
I
Analysis & Theory
Inverse of inverse is the matrix itself: (A^−1)^−1 = A.
If A and B are invertible matrices of same order, then (AB)^−1 equals
A
A^−1 B^−1
B
B^−1 A^−1
C
AB
D
None of these
Analysis & Theory
Inverse of a product: (AB)^−1 = B^−1 A^−1.
If A is an m×n matrix and O is the zero matrix of same order, then A + O equals
A
0
B
A
C
I
D
n×m
Analysis & Theory
The zero matrix is the additive identity, so A + O = A.