Indicate wheter the statement is always or sometimes false. Justify answer with logical statement or a counter example

a) If A is invertible and AB=AC , then B=C

b) If A & B are invertible, then A+ B is invertible

c) Every nxn matrix can be expressed as a product of elementary matices

d) an nxn diagonal matrix is singular if and only if the product of its diagonal entries is 0.

e) if a square matrix A satistfies A³+4A²-2A +7I =0, then so does A^T