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Chapter 4: Q18. (page 199)

Determine whether each statement is true or false.

18. Some square matrices do not have multiplicative inverses.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

­- Definition of square matrix.

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

02

­- Definition of inverse of matrix.

A matrixB is said to be an inverse of the matrix AifAB=BA=Iwhere I is an identity matrix of the same order as that of matrix Aor B.

03

­- Description of step.

A square matrixA does not have its inverse if .|A|=0

A square matrixA have its inverse if .|A|≠0

Therefore, if the determinant of the matrix is zero then the matrix will not have a multiplicative inverse.

Therefore, some square matrices which have their value of determinant as zero do not have multiplicative inverse.

04

­- State whether the given statement is true or false.

The given statement is true.

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