Determine whether the given matrices are inverses of each other. A=begin{bmatrix} 8 & 3 &-4 -6 & -2 &3-3&1&1 end{bmatrix} text{ and } B=begin{bmatrix} -1 & -1 &-1 3 & 4 &00&1&-2 end{bmatrix}

ediculeN 2021-02-04 Answered
Determine whether the given matrices are inverses of each other. A=[834623311] and B=[111340012]
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Expert Answer

Derrick
Answered 2021-02-05 Author has 94 answers
Step 1
Here we are given two matrices:
AB=[834623311][111340012]
To show that the given matrices are multiplicative inverses of each other.
Step 2
Multiply AB and BA and if both products equal the identity, then the two matrices are inverses of each other:
Find AB and BA:
AB=[834623311][111340012]
=(8(1)+33+(4)08(1)+34+(4)18(1)+30+(4)(2)(6)(1)+(2)3+30(6)(1)+(2)4+31(6)(1)+(2)0+3(2)(3)(1)+13+10(3)(1)+14+11(3)(1)+10+1(2))
=(100010691)
Step 3
Find the product BA:
BA=[111340012][834623311]
=[(1)8+(1)(6)+(1)(3)(1)3+(1)(2)+(1)1(1)(4)+(1)3+(1)138+4(6)+0(3)33+4(2)+013(4)+43+0108+1(6)+(2)(3)03+1(2)+(2)10(4)+13+(2)1]
=[120010041]
Step 4
So, the product of A and B matrices are not identity matrix. so, that the matrices are not inverse of each other.
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Jeffrey Jordon
Answered 2022-01-22 Author has 2027 answers

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