Question

If a is a square matrix of order 2 and |A| = 3 find:
(i) |adj A| =
(ii) |a(adjA)| =
(iii) A(adj A) =
(iv) |4A| =
(v) det $A^{-1}$

Answer 1

We know that.

∣Adj(AdjA)∣=∣A∣(n−1)2

                   n→ order of the square matrix.

⇒∣Adj(AdjA2)∣=∣A2∣(n−1)2

                   Given n=3

⇒∣Adj(AdjA2)∣=∣A2∣(2)2

                                   =∣A∣8

⇒∣Adj(AdjA2)∣=∣A∣8

Hence, A8 is the correct answer.