4. (a) Prove that if A is an n x n invertible matrix that satisfies the equation A2 = A then A is the identity matrix. (b) Write down a 2 x 2 matrix B that is not the identity but satisfies B² = B. %3D

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A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

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Q: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

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A: By Theorem we can say that

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Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

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A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

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Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

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A: The solution is given as

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Q: find the single matrix equal to the following

A: To find single matrix, we have to multiple the given matrix.

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Q: Is it true that the sum of invertible n x n matrices is invertible?

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A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…