Purchase Solution


Not what you're looking for?

Ask Custom Question


1) if A, B are square and AB=I_n, then det B=1/det A
2) if A, B, S are square and B=(S^-1)AS, then det B=det A
3) If A is square and (A^T)A=I_n, then det A= +/- 1
4) if A is n x n and A^T= -A, then det A= (-1)^n det A. In particular, if n is odd, then det A=0

Purchase this Solution

Solution Summary

The expert provides proofs about determinants.

Purchase this Solution

Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.