The inverse of a diagonal matrix is

A=diag⁡d1,d2,d3,……dn⇒|A|=d1×d2×d3×d4……….dnNow, Cofactor of  d1  is  d2d3....dn Cofactor of  d2 is  d1×d3×d4......dn Cofactor of  d3is d1×d2×d4......dn Cofactor of dn is d1×d2×d3……dn−1⇒ A−1=1|A|adj A=diagd1−1,d2−1,d3−1,......dn−1 Hence A−1 is also a diagonal matrix.