Prove that (cA)^-1=(1/c)A^-1 If A is an invertible matrix and c is a nonzero scalar, then cA is an invertible matrix and the above equation is true. Please show step by step how you would prove it.
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Luca B.
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You should remember that if you need to multiply a matrix with a scalar, you need to multiply each element of the matrix with the scalar, such that:
`A = v*((a,b),(c,d)) => A = ((v*a,v*b),(v*c,v*d))`
Notice that v represents the scalar(number) and A represents the matrix.
You may prove the requested identity evaluating the inverse of the new matrix `v*A` .
You need to remember that you may evaluate the inverse of a matrix only if its determinant is not equal to zero.
Supposing that the...
(The entire section contains 286 words.)
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