a. Recall that if the determinant of a matrix M (denoted |M) is not zero, then...

 

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a. Recall that if the determinant of a matrix M (denoted |M) is not zero, then M is invertable. Use the fact that |AB| = |A||B| to show that if A and B are both invertable matrices, then so is AB. (1 mark) b. Recall that the identity matrix I for dimension d is the d x d matrix that has Ij = 1 if i = j and Ij = 0 for ij. For d = 2 show that IM = MI = M for any matrix M by setting M-(2) and calculating MI and IM. You must show your work. Page 2 c. Verify that Iz = for dimension 2 by setting a 7- (8) and calculating IF. You must show your work. (1 mark) (1 mark) a. Recall that if the determinant of a matrix M (denoted |M) is not zero, then M is invertable. Use the fact that |AB| = |A||B| to show that if A and B are both invertable matrices, then so is AB. (1 mark) b. Recall that the identity matrix I for dimension d is the d x d matrix that has Ij = 1 if i = j and Ij = 0 for ij. For d = 2 show that IM = MI = M for any matrix M by setting M-(2) and calculating MI and IM. You must show your work. Page 2 c. Verify that Iz = for dimension 2 by setting a 7- (8) and calculating IF. You must show your work. (1 mark) (1 mark)