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6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix...

6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determ

6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion and see what it should equal to. Also, you should use the fact that interchanged two rows (or two columns) will introduced a negative sign when we compute the determinant (c) Compute the determinant of E (d) Do we have the equality det(EB) = det(B)det(B)?
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