12. true/false and explain your answers. a) if a is invertible then det(a)det(a-1) = 1 b) any matrix with a row of all zeros has a determinant of 1. c) if a is a skew symmetric matrix, at = -a, and a has size n x n then a must be singular if n is odd.

Answer with explanation:

(A)

It is given that, A is invertible, That is inverse of matrix exist.

That is,  , is incorrect Statement.

False

(B)

If a Matrix has , either any row or column has all entry equal to Zero, then value of Determinant is equal to 0.

Any matrix with a row of all zeros has a determinant of 1 ,is incorrect Statement.

False

(C)

The Meaning of Singular matrix is that , then Determinant of Singular Matrix is equal to Zero.

For, a n×n , matrix, whether n is Odd or even

So, the statement, If A is a skew symmetric matrix,  ,and A has size n x n then A must be singular if n is odd ,is incorrect Statement.

False

step-by-step explanation: you take each of the numbers and divide by the amount then you take the range