Question: Need help with linear algebra proofs regarding determinants and invertibility in the following image. 4 . (a) Let AEMnyn ( R ) . Matrix A

Need help with linear algebra proofs regarding determinants and invertibility in the following image.

4 . (a) Let AEMnyn ( R ) . Matrix A is said to be idempotent if A"= A. Prove that if A is idempotent , then detail or detA = 0 b ) Let A and B be nan invertible matrices satisfying AB+ BA= Oman where Onan is the man zero matrix . Prove that I must be even

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