Let A and B be any matrices. (a) Prove that if both AB and BA are...

 

Transcribed Image Text:

Let A and B be any matrices. (a) Prove that if both AB and BA are defined, then AB and BA are both square matrices. (b) Prove that if A has size m x n and ABA is defined, then B has size n x m. Suppose that A is a matrix satisfying ATA= A. Prove that A is then a symmetric matrix and that A = A². Let A and B be any matrices. (a) Prove that if both AB and BA are defined, then AB and BA are both square matrices. (b) Prove that if A has size m x n and ABA is defined, then B has size n x m. Suppose that A is a matrix satisfying ATA= A. Prove that A is then a symmetric matrix and that A = A².

Answer rating: 100% (QA)

a If AB is defined then the number of columns of A is equal to the number of rows of B Lik... View the full answer