DeterminantHard

Question

If A, B are two n × n non-singular matrices, then

Options

A.AB is non-singular
B.AB is singular
C.(AB)-1 = A-1 B-1
D.(AB)-1 does not exist

Solution

|A| ≠ 0 and  |B| ≠ 0  ⇒  |AB| ≠ 0
∴ AB is non singular.

Create a free account to view solution

View Solution Free
Topic: Determinant·Practice all Determinant questions

More Determinant Questions

If ᐃ = , then ᐃ2 is equal to -...If X = , then value of Xn is, (where n is natural number)...Let a determinant is given by A = and suppose determinant A = 6. If B = then -...The value of the determinant is -...If [a] denotes the greatest integer less than or equal to a and − 1 ≤ x < 0, 0 ≤ y < 1, 1 &#8804...