Hello, For a nonsingular matrix A and a nonnegative integer p, show what (A^p)^-1 = (A^-1)^P How to proof it.
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Originally Posted by patrick Hello, For a nonsingular matrix A and a nonnegative integer p, show what (A^p)^-1 = (A^-1)^P How to proof it. You should also say A is a square. In general (even for a group) for matrices (invertible): . Use this rule repeatedly here to get, .
Originally Posted by patrick Hello, For a nonsingular matrix A and a nonnegative integer p, show what (A^p)^-1 = (A^-1)^P How to proof it. is the multiplicative inverse of the matrix . So we know that Furthermore, this inverse is unique. So take and multiply it by . If the result is I, then the proposition is true. Therefore etc. -Dan