(a) If A is an 3 x 3 matrix and A3 = O3x3, then A O3x3 is the zero 3 x 3 matrix.) = 03x3. (Here, (b) If A, B, and C are 2 x 2 matrices and AB = AC, then B = C. (c) If A, B, and C are m x n matrices...

I need help with these True or False questions. It would be great if you can give me a simple explanation (not necessary).

Extracted text: (a) If A is an 3 x 3 matrix and A3 = O3x3, then A O3x3 is the zero 3 x 3 matrix.) = 03x3. (Here, (b) If A, B, and C are 2 x 2 matrices and AB = AC, then B = C. (c) If A, B, and C are m x n matrices and A + C = B + C, then A = B. (d) If A and B are 3 x 3 invertible matrices, then (AB)-= A-B=. (e) If A is a diagonal 3 x 3 matrix with numbers d 0 and d2 # 0 and d3 # 0 positioned along the main diagonal, then A is invertible and the inverse A- is also a diagonal matrix with numbers 1/d1 and 1/d, and 1/d, positioned along the main diagonal. (f) If A and B are non-invertible 2 x 2 matrices, then A + B is non- invertible. (g) If T: R" - R" is a lincar transformation, then T(0,) = 0m. On and 0m are the zero-vectors in R and R" respectively.) (h) If A is an invertible n xn matrix, then null(A) = null (.4") = {0,}. (Here "null" means the null space.)