let-matrix-A-n-n-and-B-n-n-satisfying-A-2-A-amp-B-2-B-then-prove-A-B-A-AB-B-AB-here-rank-

Question Number 206609 by universe last updated on 20/Apr/24

let matrix A_{n \times n} and B_{n \times n} satisfying

A^{2} = A & B^{2} = B then prove

ρ (A - B) = ρ (A - AB) + ρ (B - AB)

here ρ = rank