If A is a square matrix of order 2 and det. `A=10`, then `((tr. A)^(2)-tr. (A^(2)))` is equal to ______ .

Answer

20

Explanation

Let `A=[(a,b),(c,d)]`
`:. A^(2)=[(a,b),(c,d)][(a,b),(c,d)]`
`=[(a^(2)+bc,ab+bd),(ac+cd,bc+d^(2))]`
`:. ("tr. A")^(2)-("tr. "A^(2))=(a+d)^(2)-(a^(2)+bc+bc+d^(2))`
`=2(ad-bc)=2` det. `A=20`