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Chapter 5: Q2E (page 263)

TRUE OR FALSE? If A is an invertible matrix, then the equation(AT)-1=(A-1)Tmust hold.

Short Answer

Expert verified

The given statement is true, by the properties of the transpose of a matrix.

Step by step solution

01

Recollect the properties of the transpose of a matrix.

According to the properties of a transpose of a n脳nmatrix, ifA is an n脳ninvertible matrix, then,(AT)-1=(A-1)T.

02

Check whether the given statement is a true or false.

The given statement is if A an invertible matrix, then the equation is.

(AT)-1=(A-1)T

It is clear that, the given statement is true, by the properties of the transpose of matrices.

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