1- Given the matrix. A =
1- Calculate its inverse.
2- calculate the inverse of A^2.
3- calculate the inverse of 3A. (Hint: it may help to use the identity 3A = (3I)A).
2- Given the matrix. B =
1- Find a sequence of elementary matrices that can be used to write the matrix in row-echelon
form.
2- determine if the matrix is invertible. Justify your answer (the calculation done in part (a)
could be useful).
3- Given the matrix. M =
1- Calculate its determinant;
2- determine if the matrix is invertible. Justify your answer.
3- Calculate determine (A^2).