Finite Mathematics and Linear Algebra 102 Problem sheet 11 ... - DCU
Finite Mathematics and Linear Algebra 102 Problem sheet 11 ... - DCU
Finite Mathematics and Linear Algebra 102 Problem sheet 11 ... - DCU
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
7. A matrix A is said to be an involution is A 2 = I. Note A 2 = A · A.<br />
[ ] 1 −2<br />
(a) Show that is an involution.<br />
0 −1<br />
[ ] 5 3<br />
(b) Find the values of a <strong>and</strong> b for which the matrix is an involution.<br />
a b<br />
(c) Find six different 2 × 2 matrices which are involutions <strong>and</strong> are skew-symmetric.<br />
(d) Suppose A is an n × n matrix which is also an involution. What is A −1 .<br />
8. Let A be an n × n matrix. Let A n be the product A · A · A.. · A, the product A with itself n<br />
times. Show that (A n ) −1 = (A −1 ) n .<br />
2
Change language