Respuesta :
Inverse of matrix is a matrix derived from another matrix such that if you multiply the two you get a unit matrix. Square matrices with a an inverse are called non singular matrices while those without an inverse are called singular matrices (determinant is zero). Inverses and determinant are only calculated for square matrices. Therefore, the determinant of a singular matrix is zero and also if A and B are inverses matrices then A and B must be square matrices.
We want to see which of the given statements are true about inverse matrices.
The correct ones are:
- 2) "If A and B are inverse matrices, then A and B must be square matrices."
- 3) "The determinant of a singular matrix is equal to zero."
- 6) "Any zero matrix does not have an inverse."
- 7) "If B = A–1, then A = B–1."
First, we know that for a given square matrix A, we define the inverse matrix B as some matrix such that:
A*B = I
B*A = I
Where I is the identity matrix.
But not all square matrices have an inverse, if the determinant of the matrix is equal to zero, then the matrix does not have an inverse.
1) "All square matrices have inverses."
This is false.
2) "If A and B are inverse matrices, then A and B must be square matrices."
This is true, inverse matrices can only be square matrices.
3) "The determinant of a singular matrix is equal to zero."
A singular matrix is a non-invertible matrix, so this is true.
4) "If A and B are inverse matrices, then A + B = I."
False, if A and B are inverse matrices, then A*B = I.
5) "If A and B are inverse matrices, then det(A)xde(B)=0"
False, if A and B are invertible matrices, then neither det(A) nor det(B) can be equal to zero, so the product of these two can't be equal to zero.
6) "Any zero matrix does not have an inverse."
This is true, because the determinant of a zero matrix is equal to zero.
7) "If B = A–1, then A = B–1."
This says:
"If A is the inverse of B, then B is the inverse of A"
Which is true.
If you want to learn more, you can read:
https://brainly.com/question/18028537
