Define is subtraction of matrices commutative and associative?

Reggie

Reggie

Answered question

2020-12-15

Define is subtraction of matrices commutative and associative?

Answer & Explanation

likvau

likvau

Skilled2020-12-16Added 75 answers

Step 1
Consider three matrix A, B and C respectively.
A=[abcd],B=[efgh],C=[ijkl]
Step 2
To define whether subtraction of matrices is commutative or associative.
Step 3
Proof:
Subtraction of matrices is not commutative.
Since , AB=[abcd][efgh]
=[aebfcgdh]
And, BA=[efgh][abcd]
=[eafbgchd]
Therefore substraction of matrices is not commutative.
Step 4
Subtraction of matrices is not associative.
Since , (A+B)C=([abcd]+[efgh])[ijkl]
=[a+eib+fjc+gkd+hl]
And , (AB)+(BC)=([abcd][ijkl])+([efgh][ijkl])
=[a+e2ib+f2jc+g2kd+h2l]
So, it is also not associative.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-23Added 2605 answers

Answer is given below (on video)

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