Show that B is the inverse of A. A=begin{bmatrix}1 & -1 -1 & 2 end{bmatrix} , B=begin{bmatrix}2 & 1 1 & 1 end{bmatrix}

Reeves 2020-11-02 Answered
Show that B is the inverse of A.
A=[1112],B=[2111]
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Expert Answer

Nathanael Webber
Answered 2020-11-03 Author has 117 answers
Step 1
Given the matrices
A=[1112],B=[2111]
Show that B is the inverse of A.
Step 2
To show that two matrices are inverse it must satisfy the following condition
AB=BA=I
where I is the identity matrix
AB=[1112][2111]
AB=[(12)+(11)(11)+(11)(12)+(21)(11)+(21)]
AB=[21111121]
AB=[1001]=I
BA=[2111][1112]
BA=[(21)+(11)(21)+(12)(11)+(11)(11)+(12)]
BA=[212+2111+2]
BA=[1001]=I
So AB=BA=I
hence B is the inverse of A.
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Jeffrey Jordon
Answered 2022-01-24 Author has 2313 answers

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