# Discrete Mathematics Questions and Answers – Transpose of Matrices

This set of Discrete Mathematics Problems focuses on “Transpose of Matrices”.

1. For a matrix A, if a matrix B is obtained by changing its rows into columns and column into rows, then relation between A and B is?
a) A2 = B
b) AT = B
c) Depends on the matrix
d) None of the mentioned

Explanation: A = [aij] and B = [aji], B = AT.

2. For matrix A, (AT)T is equals to ___________
a) A
b) AT
c) Can’t say
d) None of the mentioned

Explanation: Transpose of a transposed matrix results in same matrix.

3. For matrix Aand a scalar k, (kA)T is equal to _________
a) k(A)
b) k(A)T
c) k2(A)
d) k2(A)T

Explanation: Scalar has no effect on transpose.

4. If A is a lower triangular matrix then AT is a _________
a) Lower triangular matrix
b) Upper triangular matrix
c) Null matrix
d) None of the mentioned

Explanation: By transpose a lower triangular matrix will turn to upper triangular matrix and vice – versa.

5. If matrix A and B are symmetric and AB = BA iff _________
a) AB is symmetric matrix
b) AB is an anti-symmetric matrix
c) AB is a null matrix
d) None of the mentioned

Explanation: For two symmetric matrices A and B, AB is a symmetric matrix if and only if AB = BA.

6. A matrix can be expressed as sum of symmetric and anti-symmetric matrices.
a) True
b) False

Explanation: Since A = (12)(A + AT) + ((12)(A – AT)

7. The determinant of a diagonal matrix is the product of leading diagonal’s element.
a) True
b) False

Explanation: Since in diagonal matrix all element other than diagonal are zero.

8. If for a square matrix A and B,null matrix O, (AB)T = O implies AT = O and BT = O.
a) True
b) False

Explanation: Let A=[0 1 0 0 ], B=[1 0 0 0 ] AB=O and B, AT, BT is not equal to O.

9. Let A = [aij] given by abij = (i-j)3 is a _________
a) Symmetric matrix
b) Anti-Symmetric matrix
c) Identity matrix
d) None of the mentioned

Explanation: aji =(j-i3) = -aij, A is Anti-symmetric matrix.

10. Trace of the matrix of odd ordered anti-symmetric matrix is _________
a) 0
b) 1
c) 2
d) All of the mentioned

Explanation: Since in odd ordered anti-symmetric matrix all diagonal matrix are zero.

Sanfoundry Global Education & Learning Series – Discrete Mathematics.

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