# How to deal with this kind of algebraic questions of matrix (matrices)? [closed]

How should I approach these sort of problems, like in algebraic problems of matrices, there are several restrictions with it, we cannot divide it by the matrix itself (like matrix $$A$$ in the given ques) always because $$|A|$$ might be 0 (which is the case most of the times)

For an example, what is the way to find value of the determinant given in the question?

A a nilpotent matrix with index 2.

(In this problem we have to find the value of $$|A+3I|^{50}$$, which seems exactly south to the info given). The problem is:

If $$A$$ is a $$3\times3$$ Nilpotent matrix such that $$|25A+3I|=\frac1{3^{23}}$$, then $$\det((A+3I)^{50})$$ is...

• Please use MathJax instead of including images in posts (images cannot be found by searches). Mar 18 at 17:16
• I will not say that it's a twisted mind who has conceived such an exercise, but I would never have given such a bizarre exercise to my students... Mar 18 at 17:20
• use the fact that $A$ is similar to a strictly upper triangular matrix and similarity transforms don't change determinants Mar 18 at 17:45
• @DietrichBurde please tell the answer which you are getting by your method. Mar 18 at 18:13
• @JeanMarie we have to solve these kinda problems to prepare for an exam in India. Mar 18 at 18:14