please help with these two questions with a full explanation.

1. Find an example of a 2 x 2 matrix A such that A2 75 12, A3 79 I2, and A\" : I2. Explain how you know, without calculating, that A4 must be invertible. 2. Let A be a 3 x 3 matrix with the property that det[A 3:13) 2 [at a) (a: b) (m c) where a, h, c E R are constants and :r: is a variable. Show that the transformation T given by x > Ax is one-toone if and only if all of (1,3), (3 are non-zero