Determine whether the given matrices are inverses of each other. A=[83−4−6−23−311] and B=[−1−1−134001−2]

Question

Determine whether the given matrices are inverses of each other. A=[83−4−6−23−311] and B=[−1−1−134001−2]

Derrick · Accepted Answer

Step 1  Here we are given two matrices:  AB=[83−4−6−23−311][−1−1−134001−2]  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=[83−4−6−23−311][−1−1−134001−2]  =(8(−1)+3⋅3+(−4)⋅08(−1)+3⋅4+(−4)⋅18(−1)+3⋅0+(−4)(−2)(−6)(−1)+(−2)⋅3+3⋅0(−6)(−1)+(−2)⋅4+3⋅1(−6)(−1)+(−2)⋅0+3⋅(−2)(−3)(−1)+1⋅3+1⋅0(−3)(−1)+1⋅4+1⋅1(−3)(−1)+1⋅0+1⋅(−2))  =(100010691)  Step 3  Find the product BA:   BA=[−1−1−134001−2][83−4−6−23−311]  =[(−1)⋅8+(−1)(−6)+(−1)(−3)(−1)⋅3+(−1)(−2)+(−1)⋅1(−1)(−4)+(−1)⋅3+(−1)13⋅8+4(−6)+0(−3)3⋅3+4(−2)+0⋅13(−4)+4⋅3+0⋅10⋅8+1(−6)+(−2)(−3)0⋅3+1(−2)+(−2)⋅10(−4)+1⋅3+(−2)1]  =[1−200100−41]  Step 4  So, the product of A and B matrices are not identity matrix. so, that the matrices are not inverse of each other.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

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}

Answered question

Answer & Explanation

New Questions in Precalculus