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Chapter 2: Q22E (page 108)

TRUE OR FALSE?

If A2=In, then matrixAmust be invertible.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Invertible matrix

The matrix is said to be invertible, if and only if the reduced row echelon form of the matrix has nonzero diagonal elements.

02

Compute the inverse of the matrix

Consider the condition.

A2=In鈬�A脳A=In鈭�A=A1

Thus, the inverse of the matrix exists.

Hence, the given statement is false.

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Most popular questions from this chapter

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

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