Tafuta zao la matriki hizo mbili.

Tutaweka matriki ya kwanza kama $M_1$ na ya pili kama $M_2$.

$$M_1 = \begin{pmatrix} 0 & 1 \\ 2 & p \end{pmatrix}$$ $$M_2 = \begin{pmatrix} -1.5 & -0.5 \\ p & p-2 \end{pmatrix}$$

Zao la matriki $M_1 M_2$ ni:

$$M_1 M_2 = \begin{pmatrix} (0)(-1.5) + (1)(p) & (0)(-0.5) + (1)(p-2) \\ (2)(-1.5) + (p)(p) & (2)(-0.5) + (p)(p-2) \end{pmatrix}$$ $$M_1 M_2 = \begin{pmatrix} 0 + p & 0 + p-2 \\ -3 + p^2 & -1 + p^2 - 2p \end{pmatrix}$$ $$M_1 M_2 = \begin{pmatrix} p & p-2 \\ p^2 - 3 & p^2 - 2p - 1 \end{pmatrix}$$

Kwa matriki $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$, kigezo ni $ad - bc$.
Hivyo, kwa matriki yetu $\begin{pmatrix} p & p-2 \\ p^2 - 3 & p^2 - 2p - 1 \end{pmatrix}$:

$$\det(M_1 M_2) = p(p^2 - 2p - 1) - (p-2)(p^2 - 3)$$

Panua maneno:

$$\det(M_1 M_2) = (p^3 - 2p^2 - p) - (p(p^2) - p(3) - 2(p^2) - 2(-3))$$ $$\det(M_1 M_2) = (p^3 - 2p^2 - p) - (p^3 - 3p - 2p^2 + 6)$$

Ondoa mabano:

$$\det(M_1 M_2) = p^3 - 2p^2 - p - p^3 + 3p + 2p^2 - 6$$

Unganisha vigezo vinavyofanana:

$$\det(M_1 M_2) = (p^3 - p^3) + (-2p^2 + 2p^2) + (-p + 3p) - 6$$ $$\det(M_1 M_2) = 0 + 0 + 2p - 6$$ $$\det(M_1 M_2) = 2p - 6$$

Kwa kuwa matriki ni singular, kigezo chake ni sifuri.

$$2p - 6 = 0$$

Ongeza 6 pande zote mbili:

$$2p = 6$$

Gawanya kwa 2:

$$p = \frac{6}{2}$$ $$p = 3$$

Thamani ya $p$ ni 3.

Thamani ya $p$ ni $\boxed{\text{3}}$.