This set of Discrete Mathematics online test focuses on “Operations on Matrices”.

1. Let A and B be two matrices of same order ,then state whether the given statement is true or false:

A + B = B + A

a) True

b) False

View Answer

Explanation: Matrix addition is commutative.

2. Let A and B be two matrices of same order, then state whether the given statement is true or false:

AB = BA

a) True

b) False

View Answer

Explanation: Matrix multiplication is not commutative.

3. Let A order(axb) and Border(cxd) be two matrices, then for AB to exist, correct relation is given by:

a) a = d

b) b = c

c) a = b

d) c = d

View Answer

Explanation: Matrix multiplication exists only when column of first matrix is same as rows of second i.e b = c.

4. Let A order(axb) and Border(cxd) be two matrices, then if AB exists, the order of AB is:

a) axd

b) bxc

c) axb

d) cxd

View Answer

Explanation: Matrix multiplication exists only when column of first matrix is same as rows of second i.e b = c also resultant matrix will have number of rows equal to first matrix and column equal to second matrix.

5. Let A=[a_{ij} ] be an mxn matrix and k be a scalar then kA is equal to :

a) [ka_{ij} ]_{mxn}

b) [a_{ij}/k ]_{mxn}

c) [k^{2} a_{ij} ]_{mxn}

d) None of the mentioned

View Answer

Explanation: The scalar is multiplied with each of the element of matrix A.

6. State True or False:

The matrix multiplication is distrbutive over matrix addition.

a) True

b) False

View Answer

Explanation: For matrix A, B, C, A(B+C) = AB + AC.

7. If for a square matrix A, A^{2} = A then such a matrix is known as:

a) Idempotent matrix

b) Orthagonal matrix

c) Null matrix

d) None of the mentioned

View Answer

Explanation: A sqaure matrix is called an Idempotent matrix, if A

^{2}= A.

8. State whether the given statement is True or False.

For matrix A, B.(A+B)^{T} = A^{T} + B^{T} and (AB)^{T} = A^{T}B^{T} if the orders of matrices are appropriate.

a) True

b) False

View Answer

Explanation: (A+B)

^{T}= A

^{T}+ B

^{T}is correct but (AB)

^{T}= B

^{T}A

^{T}(reversal law).

9. For matrix A, B if A – B = O, where O is a null matrix then

a) A = O

b) B = O

c) A = B

d) None of the mentioned

View Answer

Explanation: If subtraction of B from A results in null matrix this means that A is equivalent to B.

10. All the diagonal elements of a skew-symmetric matrix is:

a) 0

b) 1

c) 2

d) Any integer

View Answer

Explantion:Since for a skew symmetric matrix a

_{ij}= -a

_{ij}, this implies all diagonal elements should be zero.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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