A square matrix A is said to be a diagonal matrix if all its entries off the main diagon...

A square matrix A is said to be a diagonal matrix if all its entries off the main diagonal are zero—that is,

a _ij = 0, i = j. The entries a_ii 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 a_ii are all nonzero.

(c) In general, what is the inverse of an n × n diagonal matrix A whose main diagonal entries a_ii are all nonzero?