Question

where \( O \) denotes \( 2 \times 2 \) null matrix is f then surn of dights of th.plz help give perfect soln

Answer 1

M = \(\begin{bmatrix} a & -360 \\ b & c \\ \end{bmatrix}\)

M² = \(\begin{bmatrix} a & -360 \\ b & c \\ \end{bmatrix}\) \(\begin{bmatrix} a & -360 \\ b & c \\ \end{bmatrix}\)

= \(\begin{bmatrix} a^2&-360 b \,\,\,-360(a+c)\\ b(a+c) &\,\, c^2 -360\,b \end{bmatrix}\)

-360 (a+c) = 0 ⇒ a = -c

a² - 360 b = 0 ⇒ b = \(\frac{a^2}{360}\)

a,b,c are integer

so , for smallest positive value of b , we have 

a = 1 or a = -1

∴ b = 1/360 is smallest positive value of  b where o² is null matrix . only

needed condition is c = -a