A square matrix A is said to be a diagonal matrix if all its entries off the main diagonal are zero that is, aij = 0, i ≠ j. The entries aii on the main diagonal may or may not be zero. The multiplicative identity matrix I is an example of a diagonal matrix.
(a) Find the inverse of the 2 × 2 diagonal matrix
when a11 ≠ 0, a22 ≠ 0.
(b) Find the inverse of a 3 × 3 diagonal matrix A whose main diagonal entries aii are all nonzero.
(c) In general, what is the inverse of an n × n diagonal matrix A whose main diagonal entries aii are all nonzero?
