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Chapter 6: Q26E (page 309)

If all the entries of an invertible matrixA are integers, then the entries of A-1must be integers as well.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Matrix Definition

Matrix is aset of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥� m by n 鈥� matrix, written 鈥�m脳n .鈥�

02

To check whether the given condition is true or false

To find A-1:

For example,

A=1211is an invertible matrix with all integer entries.

By using A-1formula, however

A-1=-123212-12

Therefore, the A andA-1 both are different.

So, the given statement is false.

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Most popular questions from this chapter

There exist real invertible 3脳3 matrices A and S such that .

There exist real invertible 3脳3 matrices A andSsuch thatS-1AS=2A .

If Ais an invertible n脳n matrix, thendet(AT) must equaldet(A-1).

There exist real invertible 3脳3 matrices A andSsuch that STAS=-A

There exists a nonzero4脳4 matrixAsuch thatdetA=detA(4A).
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