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) A^T = B
c) Depends on the matrix
d) None of the mentioned
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2. For matrix A, (A^T)^T is equals to ___________
a) A
b) A^T
c) Can’t say
d) None of the mentioned
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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
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4. If A is a lower triangular matrix then A^T is a _________
a) Lower triangular matrix
b) Upper triangular matrix
c) Null matrix
d) None of the mentioned
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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
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6. A matrix can be expressed as sum of symmetric and anti-symmetric matrices.
a) True
b) False
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7. The determinant of a diagonal matrix is the product of leading diagonal’s element.
a) True
b) False
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8. If for a square matrix A and B,null matrix O, (AB)^T = O implies A^T = O and B^T = O.
a) True
b) False
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9. Let A = [a_ij] given by ab_ij = (i-j)³ is a _________
a) Symmetric matrix
b) Anti-Symmetric matrix
c) Identity matrix
d) None of the mentioned
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10. Trace of the matrix of odd ordered anti-symmetric matrix is _________
a) 0
b) 1
c) 2
d) All of the mentioned
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Sanfoundry Global Education & Learning Series – Discrete Mathematics.

To practice all areas of Discrete Mathematics Problems, here is complete set of 1000+ Multiple Choice Questions and Answers.

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