if A is a square matrix of order 3, such that / adj.A / = 64 . then find / A' / .
ans is +8 or -8
It can be explained as shown
We have
A(adj.A) = (adj.A) = |A| * I
| A(adj.A) | = | |A| * I |
|A| |adj.A | = |A| | I | ..... ( since | kA | = kn|A| )
|A| |adj.A | = |A|n * 1
| adj.A | = |A|n / |A|
This gives
| adj.A | = |A|n-1
where n is the order of the matrix.
So in this question
| adj.A | = |A|n-1 64 = | A | 2 |A| = +8 or -8