Help! Matrix

[Mathayom]

I don't know how to solve letter b) in the photo. Thank you

 

[Deleted member 4993]

I don't know how to solve letter b) in the photo. Thank you

If I were to do this problem, I would first calculate |A| and |B|. I am assuming |A| = determinant of A

I am assuming that you know the process of calculating the determinant of a matrix.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Mathayom]

Thank you so Much! I was doing the wrong thing the whole time. I even apply properties for inverse matrix, I never thought about using the determinants of both matrix! Such a big help! Thank you. I got it

 

[Steven G]

Assuming that AC can be the Identity matrix then just dotting the 1st row of A with the 1st column of C gives you that 4+2k=1. You can easily solve for k.

Since AC = I for the correct value of k, then A^-1 = C. So (A²)^-1 = (A^-1)² = C².

To see that (A²)^-1 = (A^-1)² just note that (A²)^-1 = (A*A)^-1 = A^-1*A^-1 = (A^-1)²