Question

If  A is non singular matrix then prove that  A-¹=AdjA/|A|

Answer 1

Answer:

I suggest that you write these equations on paper incase you find them clumsy.

It is easy to see that |kA| = (k^n)|A| where k is a constant and n is the order of the square matrix A.We know that |A^-1| is 1/|A|.Since A^-1 is (1/|A|) adj (A),we get |A^-1| = (1/|A|)^n |adj(A)| which implies |A|^(n)/|A| is |adj(A)|.

So |A|^(n-1) = |adj(A)|.

QED