Find the inverse of the matrix [6, 7] [-6, 7] if it exists

For any square matrix A, if it is invertible, its inverse is given by

where adj(A) is the so-called adjugate matrix, which is the transpose of the cofactor matrix of A. If you don't know what that is, that's not terribly important. What is important is that the inverse does not exist if the determinant, det(A), is zero.

We have

so the inverse does indeed exist. (And we eliminate D as an answer.)

From the given choices, it's quite clear that C must the correct answer, since we know det(A) = 84, and we can easily confirm that

so that multiplying by 1/84 recovers the identity matrix.

70.30

step-by-step explanation: