State True or False for the statements
(aA)^-1 = (1/a) A^-1, where a is any real number and A is a square matrix.

Question

State True or False for the statements (aA) -1 = (1/a) A -1 , where a is any real number and A is a square matrix.

Philoid · Accepted Answer

False

We know that if A is a non-singular square matrix, then for any scalar a, aA is invertible such that

i.e. , where a is any non-zero scalar.

In the above statement a is any real number So, we can conclude that above statement is false.

State True or False for the statements(aA)-1 = (1/a) A-1, where a is any real number and A is a square matrix.