Matrices - Basic

A classroom has a seating arrangement where the number of rows is equal to the number of columns. In this scenario, when is the classroom considered to have a square seating arrangement?

• The number of rows is equal to the number of columns

• The number of rows is greater than the number of columns

• The number of rows is less than the number of columns

• None of these

For a square matrix, the sum of the diagonal elements is called the _______of the matrix.

• determinant

• trace

• zero

• None of these

A matrix is said to be scalar matrix if all the diagonal elements of the square matrices are

• 0

• 1

• equal

• None of these

Two matrices can be added if they are

• of same size

• square matrices

• row matrices

• column matrices

If a classroom seating arrangement is obtained by changing the respective rows into columns, then we get________ of the classroom.

• Negative

• Inverse

• Transpose

• None of these

In a mathematics class, a square matrix is considered symmetric if

• The transpose of the matrix is equal to the matrix itself

• The transpose of the matrix is equal to the negative of the matrix

• The matrix is equal to the zero matrix

• None of these

In a robotics competition, a robot's movement matrix is considered skew-symmetric if

• The robot's movement matrix transposed is equal to the negative of the original matrix

• The robot's movement matrix transposed is equal to the original matrix

• The robot's movement matrix is a zero matrix

• None of these

If the order of a matrix A is 2 x 4 and B is of the matrix 4 x 7, then AB is of order

• 2 x 7

• 7 x 2

• 2 x 2

• 7 x 7

In a school competition, Aarav was asked to find the diagonal elements of a skew-symmetric matrix. What are the diagonal elements of a skew-symmetric matrix always?

• 1

• 0

• equal

• None of these

If for two matrices A and B, AB = 0, then

• A = 0 or B = 0

• both are O

• none of them may be O

• None of these