Answer :
(a) The determinant of I + A is 1 + det A is false
(b) The determinant of ABC is |A||B||C| is true
(c) The determinant of 4A is 4|A| is false
(d) The determinant of AB − BA is zero is false
Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule. They help to find the adjoint, and inverse of a matrix.
(a) The determinant of I + A is 1 + det A.
False, for example with A = I being the two-by-two identity matrix. Then det(I +A) = det(2I) = 4 and 1 + det A = 2.
(b) The determinant of ABC is |A||B||C|.
True, the determinant of a product is the product of the determinants.
(c) The determinant of 4A is 4|A|.
False, the determinant of 4A is [tex]4^{n} |A|[/tex] if A is an n by n matrix.
(d) The determinant of AB − BA is zero.
False, for example
[tex]A=\left[\begin{array}{ccc}0&0\\0&1\\\end{array}\right] \\B=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
Then,
[tex]AB-BA = \left[\begin{array}{ccc}0&0\\c&d\\\end{array}\right] - \left[\begin{array}{ccc}0&b\\0&d\\\end{array}\right]= \left[\begin{array}{ccc}0&-b\\c&0\\\end{array}\right][/tex]
with determinant bc. This is not zero unless b = 0 or c = 0.
To know more about determinants visit: brainly.com/question/13369636
#SPJ4
