Q16. - Algebra 2

Question

Determine whether each statement is true or false.

16. Only square matrices have multiplicative identities.

Step-by-Step Solution

Answer

The given statement is true.

Step 1 ­- Definition of square matrix.

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

Step 2 ­- 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 matrixA is a square matrix of the same order as that of .I

Therefore, only square matrices have multiplicative identities because the multiplications of the matrix and the identity matrix will only be defined when the matrix is a square matrix.

Step 3 ­- State whether the given statement is true or false.

The given statement is true.