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Matrices and Determinants Quiz 1

Leave a Comment / By Ankur Negi / 30 November 2025

Welcome to your Matrices Quiz 1

1. Which if the following represents a column matrix?

[a_{ij}]_{m \times n}

[a_{ij}]_{m \times 1}

[a_{ij}]_{1 \times n}

[a_{ij}]_{1 \times 1}

None

2. Which of the following is true?

(A B)' = A' B'

(A B)' = \frac{1}{AB}

(A B)' = B' A'

None of these

None

3. A is a skew symmetric matrix if

A' = A

A' = \frac{1}{A}

A = A + A'

A' = -A

None

4. Which of the following is true?

(A+B)' = A' + B'

(A+B)' = A' - B'

(A+B)' = \frac{1}{A + B}

(A+B)' = \frac{1}{A} + \frac{1}{B}

None

5. For matrix $A = [a_{ij}]_{m \times n}$ its transpose is

A' = [a_{ij}]_{m \times n}

A' = [a_{ji}]_{m \times n}

A' = [a_{ij}]_{n \times m}

A' = [a_{ji}]_{n \times m}

None

6. Given that $M_{ij}$ is the minor of the element $a_{ij}$ then its co-factor $A_{ij}$ is given by the formula

A_{ij} = \frac{1}{M_{ij}}

A_{ij} = (-1)^{i+j} M_{ij}

A_{ij} = (-2)^{i+j} M_{ij}

A_{ij} = \frac{-1^{i+j}}{M_{ij}}

None

7. Which of the following gives the determinant of a matrix A?

a_{11}A_{11} + a_{22}A_{12} + a_{33}A_{13}

a_{11}A_{11} + a_{22}A_{22} + a_{33}A_{33}

a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}

None of These

None

8 Which of the following is correct?

A^{-1} = \frac{1}{|A|} (adj A)

A^{-1} = |A| (adj A)

A^{-1} = \frac{1}{|A|} (A)

A^{-1} = \frac{1}{|A|} (M_{ij})

None

9. $a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23}$ =

-1

0

1

|A|

None

10. Which of the following is true?

|adj(A)| = |A|

|adj(A)| = |A|^n

|adj(A)| = |A|^{n-1}

|adj(A)|^n = |A|

None

Time's up