7.) Find X so that for any 3 × 3 real matrix A you get AX = XA = A [Hint : what property is being exhibited by real number p so that for any real w we get wp = pw = w then interpret for matrices.] 1 8.) Consider K = 1 −1 1 −1 then we get K2 = 0 Does this hold for real numbers? Motivate.
17.
X=
Its equivalent to identify property of multiplication in real numbers where:
wp=pw=w given p= 1
Given K=
K2 =
=
The above is not true for real numbers.
Only a square of "0" will give a zero
00=0.
18.
-If ab=0, either a=0 or b=0
-Products of two non-zero numbers is always non-zero
But products of two non-zero matrices can be zero matrix
Using K given above
K=
That is K
K2=(K)(K)
=
=
=0 (Null matrix)
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