250+ TOP MCQs on Matrix Multiplication using Recursion and Answers

Data Structures & Algorithms Multiple Choice Questions on “Matrix Multiplication using Recursion”.

1. If Matrix A is of order X*Y and Matrix B is of order M*N, then what is the order of the Matrix A*B given that Y=M?
a) Y*N
b) X*M
c) X*N
d) Y*M
Answer: c
Clarification: The Matrix A*B is of order X*N as it is given that Y=M i.e. number of columns in Matrix A is equal to total number of rows in matrix B. So the Matrix A*B must have X number of rows and N number of columns.

2. How many recursive calls are there in Recursive matrix multiplication through Simple Divide and Conquer Method?
a) 2
b) 6
c) 9
d) 8

Answer: d
Clarification: For the multiplication two square matrix recursively using Simple Divide and Conquer Method, there are 8 recursive calls performed for high time complexity.

3. What is the time complexity of matrix multiplied recursively by Divide and Conquer Method?
a) O(n)
b) O(n²)
c) O(n³)
d) O(n!)

Answer: c
Clarification: The time complexity of recursive multiplication of two square matrices by the Divide and Conquer method is found to be O(n³) since there are total of 8 recursive calls.

4. What is the time complexity of matrix multiplied recursively by Strassen’s Method?
a) O(n^log7)
b) O(n²)
c) O(n³)
d) O(n!)

Answer: a
Clarification: The time complexity of recursive multiplication of two square matrices by Strassen’s Method is found to be O(n^log7) since there are total 7 recursive calls.

5. How many recursive calls are there in Recursive matrix multiplication by Strassen’s Method?
a) 5
b) 7
c) 8
d) 4

Answer: b
Clarification: For the multiplication two square matrix recursively using Strassen’s Method, there are 7 recursive calls performed for high time complexity.

6. Matrix A is of order 3*4 and Matrix B is of order 4*5. How many elements will be there in a matrix A*B multiplied recursively.
a) 12
b) 15
c) 16
d) 20

Answer: b
Clarification: The resultant matrix will be of order 3*5 when multiplied recursively and therefore the matrix will have 3*5=15 elements.

7. If Matrix X is of order A*B and Matrix Y is of order C*D, and B=C then the order of the Matrix X*Y is A*D?
a) True
b) False

Answer: a
Clarification: Given that B=C, so the two matrix can be recursively multiplied. Therefore, the order of the Matrix X*Y is A*D.

8. What is the time complexity of the fastest known matrix multiplication algorithm?
a) O(n^log7)
b) O(n^2.37)
c) O(n³)
d) O(n!)

Answer: b
Clarification: The Coppersmith-Winograd algorithm multiplies the matrices in O(n^2.37) time. Several improvements have been made in the algorithm since 2010.

9. Is Coppersmith-Winograd algorithm better than Strassen’s algorithm in terms of time complexity?
a) True
b) False

Answer: a
Clarification: Since The Coppersmith-Winograd algorithm multiplies the matrices in O(n^2.37) time. The time complexity of recursive multiplication of two square matrices by Strassen’s Method is found to be O(n^2.80). Therefore, Coppersmith-Winograd algorithm better than Strassen’s algorithm in terms of time complexity.

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