• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Linear Algebra With Applications
Found in: Page 263
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.


Short Answer

TRUE OR FALSE? The equation det(AT)=det(A) holds for all 2×2 matrices A.

The given statement is true.

See the step by step solution

Step by Step Solution

 Step 1: Definition of the determinant.

Suppose A=[abcd] is a 2×2 matrix.

Then the determinant of matrix A is defined as,

det(A)=[abcd] =ad-bc

 Step 2: Check whether the given statement is a true or false.

The given statement is the equation detAT=detA holds for all 2×2matrix A.

Let A=abcd.



Find det AT,detA

detA=abcd =ad-bcdetAT=acbdc =ad-cd

This is clear that, the equation detAT=detAis holds for all 2×2 matrix A

Then the given statement is true.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.