# Worksheet: Transpose of a Matrix

In this worksheet, we will practice finding the transpose of a matrix, elements of a given row and column after transposing, and a matrix's dimensions after transposing.

**Q1: **

Find the transpose of the matrix .

- A
- B
- C
- D

**Q2: **

If and , what is ?

- A
- B
- C
- D

**Q3: **

Given that what is ?

- A
- B
- C
- D

**Q4: **

Given the matrix find .

- A
- B
- C
- D

**Q5: **

Consider the matrices Is it true that ?

- AYes
- BNo

**Q6: **

What operation must be performed on the matrix to get the matrix ? How does this operation affect the value of the determinant?

- AThe second matrix is the first matrix with the columns swapped. The determinant of the second matrix is times the determinant of the first matrix.
- BThe second matrix is the inverse of the first. The determinant of the second matrix is the reciprocal of the determinant of the first matrix.
- CThe second matrix is the first matrix with the rows swapped. The determinant of the second matrix is times the determinant of the first matrix.
- DThe second matrix is the transpose of the first. The determinant of the second matrix is the same as the determinant of the first matrix.
- EThe second matrix is the inverse of the first. The determinant of the second matrix is the same as the determinant of the first matrix.

**Q7: **

If is a matrix of order , then what is the order of the matrix ?

- A
- B
- C
- D

**Q8: **

Given that determine the value of .

- A20
- B8
- C
- D0

**Q9: **

Given the shown matrices, determine whether .

- Ayes
- Bno

**Q10: **

Find the transpose of the matrix .

- A
- B
- C
- D

**Q11: **

Find the transpose of the matrix .

- A
- B
- C
- D

**Q12: **

Find the transpose of the matrix .

- A
- B
- C
- D