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Prove that A is invertible if a 6= 0 and a 6= b (find the pivots and A 1 ): A = a b b a

Chapter 1, Problem 1.6.42

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QUESTION:

Prove that A is invertible if a 6= 0 and a 6= b (find the pivots and A 1 ): A = a b b a a b a a a

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QUESTION:

Prove that A is invertible if a 6= 0 and a 6= b (find the pivots and A 1 ): A = a b b a a b a a a

ANSWER:

Step 1 of 2

Given matrix is

To prove that A is invertible if .

Let us find the determinant of A.

If , then . It implies that A is nonsingular for and therefore, it is not invertible.

Hence, the given matrix A is invertible if .

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