## 1. Which of the following matrices is a square matrix?

### Answer:

### Explanation:

A square matrix has an equal number of rows and columns. Hence, a 4×4 matrix is a square matrix.

## 2. The order of the matrix [[1,2],[3,4],[5,6]] is:

### Answer:

### Explanation:

The matrix has 3 rows and 2 columns, so its order is 3×2.

## 3. If A is a matrix of order 2×3, then the total number of elements in matrix A is:

### Answer:

### Explanation:

For a matrix of order 2×3, there are 2 rows and 3 columns, so total elements = 2×3 = 6.

## 4. Two matrices are said to be equal if:

### Answer:

### Explanation:

Two matrices are equal if they have the same order and their corresponding elements are equal.

## 5. The zero matrix of order 2×2 is:

### Answer:

### Explanation:

A zero matrix has all its elements as zero.

## 6. If A and B are matrices of the same order, then (A+B)' is:

### Answer:

### Explanation:

The transpose of the sum of two matrices is the sum of their transposes.

## 7. The matrix [[1,2],[3,4]] is of type:

### Answer:

### Explanation:

The given matrix has equal numbers of rows and columns, making it a square matrix.

## 8. If A is a matrix of order 3×2, the order of its transpose A' is:

### Answer:

### Explanation:

The transpose of a matrix interchanges its rows with columns.

## 9. The matrix which has only one row is called:

### Answer:

### Explanation:

A matrix with a single row is termed a row matrix.

## 10. The sum of the diagonal elements of a matrix is called:

### Answer:

### Explanation:

The sum of the diagonal elements of a matrix is termed its trace.

## 11. The element situated in the third row and second column of the matrix [[1,2,3],[4,5,6],[7,8,9]] is:

### Answer:

### Explanation:

The element in the third row and second column is 8.

## 12. If A' is the transpose of A, then (A')' is:

### Answer:

### Explanation:

Taking the transpose twice results in the original matrix.

## 13. For any square matrix A, (A+A') is always:

### Answer:

### Explanation:

A matrix is symmetric if it is equal to its transpose.

## 14. A matrix in which all elements are zero except the diagonal elements is called:

### Answer:

### Explanation:

A matrix with non-zero elements only on its diagonal is a diagonal matrix.

## 15. If A is an identity matrix of order 3×3, then the sum of all its elements is:

### Answer:

### Explanation:

The identity matrix has ones on the diagonal and zeros elsewhere.

## 16. A square matrix in which all the elements below its main diagonal are zero is called:

### Answer:

### Explanation:

An upper triangular matrix has all elements below the diagonal as zero.

## 17. If A and B are matrices of order 3×3, then the order of the product matrix AB is:

### Answer:

### Explanation:

The product of two matrices has the order of the first matrix's rows by the second matrix's columns.

## 18. The number of rows in a column matrix of order 7×1 is:

### Answer:

### Explanation:

A column matrix has a single column, and in this case, 7 rows.

## 19. If two matrices A and B are conformable for multiplication, then:

### Answer:

### Explanation:

For two matrices to be conformable for multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.

## 20. If a matrix has only one column, it is called:

### Answer:

### Explanation:

A matrix with a single column is termed a column matrix.