Explain why the condition a = 0 guarantees that A is not invert- ible.

Question

Let A = | 1 a 1

c 0 2

1 a 1/c + 1 |

, where c does not equal 0 and a ∈ R.

(a) Explain why the condition a = 0 guarantees that A is not invertible. No calculations are necessary here, it is possible to explain the answer by referring to a result (or results).

(b) Now assume a not equal to 0, and that the inverse of A exists. Use row operations to calculate A^−1

Answer 1

If a = 0 then a is not invertible because 1/a = 1/0, which is undefined.