Problems:
Mathematics - Matrices - Invertible Matrices
Question-1
(a) If A is invertible and AB = AC, prove that B = C.
Question-2
(a) If a square matrix A has the property that row 1 + row 2 = row 3, clearly explain why the matrix A is not invertible.
(b) If any square matrix B has the property that one row equals the sum of multiples of the other rows, clearly explain why the matrix B is not invertible.
In class, we will show (Section 3.5) that AB is an invertible matrix if and only if A and B are both invertible. In some sense, invertibility is preserved when multiplying invertible matrices together.