please help with those and try to keep the answer short and dont use ChatGpt

Let T1 and T2 be linear transformations given by T1([12])=[21+321+62]T2([12])=[41521+52] Find the matrix A such that (a) T1(T2(x))=Ax (b) T2(T1(x))=Ax (d) T2(T2(x))=Ax Suppose that T is a linear transformation and that T(u1) and T(u2) are linearly independent. Prove that u1 and u2 must be linearly independent. 22 matrices A,B, and C that are nonzero, where A=B but AC=BC (a) Suppose that E1 and E2 are two elementary matrices. Then E1E2=y E2E1. (b) If E is an nn elementary matrix corresponding to interchanging two rows, then E2=In. Let A be an nm matrix. (a) What are the dimensions of ATA ? (b) Show that ATA is symmetric