The product of any matrix by the scalar ......... Is the null matrix.

The rank of a null matrix is

The rank of a null matrix is

If the product of two non null square matrices is a null matrix; show that both of them must be singular matrices.

Multiplication of a matrix by a scalar and its properties

Give examples to show that : AB is a null matrix, where neither A nor B is a null matrix.

Give an example of a matrix which is a scalar matrix which is not a unit matrix.

If an idempotent matrix is also skew symmetric then it can not be 1 an involutary matrix 2 an identity matrix 3 an orthogonal matrix 4 a null matrix.

Give an example of a row matrix which is also a column matrix a diagonal matrix which is not scalar (iii) a triangular matrix.