If A is an 3 × 3 non-singular matrix such that AA' = A'A and B = A

Engineering

Mathematics

Inverse of a Matrix

Question

If A is an 3 × 3 non-singular matrix such that AA' = A'A and B = A^–1A', then BB' equals

B^–1

(B^–1)'

I + B

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BB^T = A^–1A^T (A^–1A^T)^T

= A^–1A^T A(A^–1)^T = A^–1AA^T(A^–1)T

= A^T (A^–1)^T = (A^–1A)^T = I^T = I.