Which of the following statements are true about inverse matrices?All square matrices have inverses.If A and B are inverse matrices, then A and B must be square matrices.The determinant of a singular matrix is equal to zero.If A and B are inverse matrices, then A + B = I.If A and B are inverse matrices, then det(A)xde(B)=0Any zero matrix does not have an inverse.If B = Aβ1, then A = Bβ1.
Question
Answer:
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.
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