Properties of Inverse of a Square Matrix · Square matrix A is invertible if and only if |A|≠ 0 · (A-1)-1=A · (A')-1 = (A-1)' · (AB)-1 = B-1A-1 In general ( A1A1A1 ...
Properties of Matrices Inverse ... It is noted that in order to find the matrix inverse, the square matrix should be non-singular whose determinant value does not ...
Properties of Inverses · If A is nonsingular, then so is A -1 and (A -1 ) -1 = A · If A and B are nonsingular matrices, then AB is nonsingular and (AB) -1 = B -1 A · If ...
If A - 1 = B, then A (col k of B) = e k
If A has an inverse matrix, then there is only one inverse matrix.
If A 1 and A 2 have inverses, then A 1 A 2 has an inverse and (A 1 A 2 ) - 1 = A 1 - 1 A 2 - 1
If A has an inverse, then x = A - 1 d is the solution of Ax = d and this is the only solution.