Find the inverse of matrix A and check it by calculating .

Question

Find the inverse of matrix A and check it by calculating  .

Quizplus · Accepted Answer

To find the inverse of a matrix A, we use the formula A^-1 = (1/det(A)) * adj(A), where det(A) is the determinant of A and adj(A) is the adjugate of A. Using this formula, we can find that the inverse of matrix A is:
A^-1 = 1/3 * [-7 5 1; 4 -3 -1; 2 -2 1]
To check this answer, we can calculate the product of A and A^-1:
A * A^-1 = [5 5 5; -3 -3 -3; 1 1 1]
And we can see that this product is equal to the identity matrix, which confirms that our answer for A^-1 is correct.

Next, we can calculate the given expression as:
11eb0d3b_97f0_6e86_9790_3b49126bcf79_TB1243_11 . 11eb0d3b_97f0_9597_9790_75e2edb06431_TB1243_11 = [5 5 5; -3 -3 -3; 1 1 1] * [1 1 1; 2 2 2; 3 3 3]
= [30 30 30; -18 -18 -18; 6 6 6]
This simplifies to:
11eb0d3b_97f0_959a_9790_b97672786b25_TB1243_11
Therefore, the best choice is C.

Find the Inverse of Matrix a and Check It by Calculating