Q17. - Algebra 2

Question

Determine whether each statement is true or false.

17. Only square matrices have multiplicative inverses.

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 ­- Definition of inverse of matrix.

A matrixB is said to be an inverse of the matrix Aif$\mathbf{AB}\mathbf{=}\mathbf{BA}\mathbf{=}\mathbf{I}$ where/ is an identity matrix of the same order as that of matrixA orB .

Step 3 ­- Description of step.

As it can be noticed that the productsAB andBA will be defined and will be of same order only if both matricesA andB are square matrices of same order.

Therefore, the multiplicative inverses will be possible only for the square matrices.

Step 4 ­- State whether the given statement is true or false.

The given statement is true.