find the values of a and b given that matrix A=

Question

[a -4 -6]
[-8 5 7]
[-5 3 4]
is the inverse of matrix B =
[1 2 -2]
[3 b 1]
[-1 1 -3]
It would really help if you showed how you did it.
Thanks a lot!

Answer 1

I trust you know how to multiply two matrices

and I trust that you know that if you multiply any matrix by its inverse you get the identity matrix, namely
1 0 0
0 1 0
0 0 1

so using the first row of matrix A and the first column of matrix B you get
a - 12 + 6 = 1
a = 7

then second row of A by second column of B gives us
-16 + 5b + 7 = 1
b = 2