Question

If a is an invertible matrix of order 2 and det

a.= 4 then write the value of det a 1

Answer 1

We know that A^(-1) = adjA / |A|
so |A^(-1)| = |adj A | /|A| = |A|/ |A| = 1
{|adjA| = |A|^ (n-1) where n is the order of matrix}

Answer 2

given matrix 2×2,

| A|= 4

A. A^-1 = I

|AA^-1|=I

|A|.|A^-1|=|I|

|A|.|A^-1|= 1

| A^-1|= 1/|A|

|A^-1|= 1/4