For an m n matrix A and its pseudo-inverse A , show that A = AAA and A = AAA in each of the following cases. (a) A is tall with linearly independent...

For an m × n matrix A and its pseudo-inverse A† , show that A = AA†A and A† = A†AA† in each of the following cases.

(a) A is tall with linearly independent columns.

(b) A is wide with linearly independent rows

(c) A is square and invertible.