Question

Determine whether each statement is true or false.

19. Some square matrices do not have multiplicative identities.

Short answer

The given statement is false.

Step-by-step solution

­- Definition of square matrix.

A square matrix is a matrix in which number of rows is equal to number of columns.

­- Description of step.

The multiplicative identity of a matrixA is an identity matrix I of the same order if .$AI=IA=A$

It can be noticed that an identity matrix is a square matrix and the multiplication$AI$ and IA of two matrices will be defined only when the matrix A is a square matrix of the same order as that of /.

There can be no square matrix which when multiplied with an identity matrix do not yield the given matrix.

Therefore, no such square matrix is possible which do not have multiplicative identities.

­- State whether the given statement is true or false.

The given statement is false