By applying Fundamental Theorem of group homomorphism, show that the quotient groups GL(n, R)/SL(n, R) is isomorphic to the multiplicative group (R\{0}, ·) of non-zero real numbers. (Here GL(n, R) denotes the general linear group of all n × n matrices over R and GL(n, R) denotes the special linear group of all n × n matrices over R.)

By applying Fundamental Theorem of group homomorphism, show that the quotient groups GL(n, R)/SL(n, R) is isomorphic to the multiplicative group (R\{0}, ·) of non-zero real numbers. (Here GL(n, R) denotes the general linear group of all n × n matrices over R and GL(n, R) denotes the special linear group of all
n × n matrices over R.)