Let M(n, R) denote the set of n x n matrices with real entries. We define...

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Let M(n, R) denote the set of n x n matrices with real entries. We define the General Liner Group of degree n over the real numbers by GL(n, R):= {MEM(n, R) | Det(M) #0}. GL(n, R) is a group under matrix multiplication. Let H(n, R):= {ME GL(n, R) | Det(M) = 2k for some k Z}. Show that H(n, R) is a subgroup of GL(n, R). Let M(n, R) denote the set of n x n matrices with real entries. We define the General Liner Group of degree n over the real numbers by GL(n, R):= {MEM(n, R) | Det(M) #0}. GL(n, R) is a group under matrix multiplication. Let H(n, R):= {ME GL(n, R) | Det(M) = 2k for some k Z}. Show that H(n, R) is a subgroup of GL(n, R).

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