Question

Evaluate |A|^2-5|A|+1, if A=\(\begin{bmatrix}7&4\\5&5\end{bmatrix}\)

(a) 161

(b) 251

(c) 150

(d) 151

I have been asked this question in an internship interview.

This interesting question is from Determinant in section Determinants of Mathematics – Class 12

Answer 1

Right answer is (d) 151

The best I can explain: Given that, A=\(\begin{bmatrix}7&4\\5&5\end{bmatrix}\)

|A|=(7(5)-5(4))=35-20=15

|A|^2-5|A|+1=(15)^2-5(15)+1=225-75+1=151.