Hi guys,
Hope this is in the right areas - 'Search' tells me matrix questions are all over the place so I apologies if this should be elsewhere.
We are given this equation: A^-1BCD^-1 = I
A, B, C and D are all non-singular & I is an identity matrix.
It asks me to find C given 5 multiple choices.
1. (D^-1B)^-1
2. DA^-1
3. (A^-1D)^-1
4. D^-1B
5. A^-1BD^-1A
I want to understand conceptually how this works - it rarely seems to be covered in theory and seems mostly to be implied by completing the questions so if anyone has the time to explain that would be much more helpful than just the answer (thanks in advance if you have the time).
I understand that A and its inverse multiply to give I and am temped to think that if there are two inverses on the left of the equation (A^-1 & D^-1) then B and C must be the original matrices (A & D) so that when multiplied together they essential cancel to give the identity matrix. Is that the best way to approach this kind of questions? Is it a process of making the right combination of matrix opposites until they cancel to give I?
I have tried substituting in the answers but I am again not sure whether it works the way I am inferring it works.
Hope thats enough information - Thanks for any help with this one!
Hope this is in the right areas - 'Search' tells me matrix questions are all over the place so I apologies if this should be elsewhere.
We are given this equation: A^-1BCD^-1 = I
A, B, C and D are all non-singular & I is an identity matrix.
It asks me to find C given 5 multiple choices.
1. (D^-1B)^-1
2. DA^-1
3. (A^-1D)^-1
4. D^-1B
5. A^-1BD^-1A
I want to understand conceptually how this works - it rarely seems to be covered in theory and seems mostly to be implied by completing the questions so if anyone has the time to explain that would be much more helpful than just the answer (thanks in advance if you have the time).
I understand that A and its inverse multiply to give I and am temped to think that if there are two inverses on the left of the equation (A^-1 & D^-1) then B and C must be the original matrices (A & D) so that when multiplied together they essential cancel to give the identity matrix. Is that the best way to approach this kind of questions? Is it a process of making the right combination of matrix opposites until they cancel to give I?
I have tried substituting in the answers but I am again not sure whether it works the way I am inferring it works.
Hope thats enough information - Thanks for any help with this one!