Find which of the following matrices is an inverse to the matrix A below if any. Matrix I : Matrix II : Matrix III :
A) Each of the matrices I and III is an inverse of A.
B) Each of the matrices I and II is an inverse of A.
C) Each of the matrices II and III is an inverse of A.
D) Matrix II is an inverse of A.
E) None of the matrices is an inverse of A.

Question

Find which of the following matrices is an inverse to the matrix A below if any.  Matrix I :  Matrix II :  Matrix III : 
A) Each of the matrices I and III is an inverse of A. 
B) Each of the matrices I and II is an inverse of A. 
C) Each of the matrices II and III is an inverse of A. 
D) Matrix II is an inverse of A. 
E) None of the matrices is an inverse of A.

Quizplus · Accepted Answer

To check if a matrix B is an inverse of matrix A, we need to verify if AB = BA = I, where I is the identity matrix.
Calculating the product AB for each matrix gives:
Matrix I: 
AB = 11ea89fe_4bc8_ca3e_9fff_8b90a94a09f6_TB2036_00 (not equal to I)
Therefore, matrix I is not an inverse of A.
Matrix II:
AB = 11ea89fe_4bc8_ca41_9fff_37e90276673f_TB2036_00
BA = 11ea89fe_4bc8_ca41_9fff_37e90276673f_TB2036_00
Both products are equal to the identity matrix. Therefore, matrix II is an inverse of A.
Matrix III:
AB = 11ea89fe_4bc8_ca3d_9fff_15807c001e39_TB2036_00 (not equal to I)
Therefore, matrix III is not an inverse of A.

So, the only possible choice is D, matrix II is an inverse of A.

Find Which of the Following Matrices Is an Inverse to the Matrix